Daily Papers

We investigate the propagation of fast radio bursts (FRBs) through magnetar magnetospheres. Previous work showed that, in the inner magnetosphere, GHz radio waves propagate as fast magnetosonic waves and undergo resonant three-wave interactions that transfer their energy into trapped Alfvén waves. Using three-dimensional force-free electrodynamics simulations, we demonstrate that FRBs would excite Alfvénic fluctuations, leading to strong nonlinear attenuation of the radio signal. In quiescent dipolar magnetospheres, the nonlinear decay stays efficient within sim10--100 magnetar radii; charge starvation of the excited Alfvén waves stops the decay at larger radii. For FRBs propagating within relativistic magnetic outflows launched during magnetospheric eruptions, three-wave interactions remain efficient and constrain the escape radius to gtrsim10^2--10^3 magnetar radii for luminous bursts. Our results confirm that nonlinear plasma processes strongly limit the escape of FRBs from the inner magnetospheres of magnetars.

This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation. The Waveguide Solution Theorem provides an elegant way to solve waveguide problems, while The Schrodinger Solution Theorem connects the Maxwell's equations with the two-dimensional Schrodinger equation. By utilizing The Schrodinger Solution Theorem, a precise formula for spatiotemporal diffraction of the Maxwell's equations is derived, which allows for the reconstruction of electromagnetic waves throughout space and time based on the field distribution on the diffraction screen. And finally, by studying some relevant contour integrals, two additional simple but beautiful mathematical theorems that are necessarily satisfied by electromagnetic field in any source-free region are derived.

This manuscript presents an historical perspective prepared by Barry Ninham and Colin Pask in 1969 on the connection between quantum electrodynamics theory and nucleon interactions. A new theory of strong interactions based on electromagnetic considerations is proposed. Energy and force range magnitudes are correctly given. A new theory of the pion emerges and the pion mass and lifetime are calculated. No strong interaction coupling constant is required.

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4+1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field.

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical methods have been applied successfully in the past, the primary challenge in solving these equations arises from the frequency of electromagnetic fields, which depends on the shape and size of the objects to be resolved. Since the domain of influence for these equations is compactly supported, even a small perturbation in frequency necessitates a new discretization of Maxwell's equations, resulting in substantial computational costs. In this work, we investigate the potential of neural operators, particularly the Deep Operator Network (DeepONet) and its variants, as a surrogate model for Maxwell's equations. Existing DeepONet implementations are restricted to real-valued data in R^n, but since the time-harmonic Maxwell's equations yield solutions in the complex domain C^n, a specialized architecture is required to handle complex algebra. We propose a formulation of DeepONet for complex data, define the forward pass in the complex domain, and adopt a reparametrized version of DeepONet for more efficient training. We also propose a unified framework to combine a plurality of DeepONets, trained for multiple electromagnetic field components, to incorporate the boundary condition. We conduct computational experiments on a 3D metallic sphere without singularities and on a metallic almond-shaped target to demonstrate the effectiveness of the proposed method for problems involving singularity-prone solutions. As shown by computational experiments, our method significantly enhances the efficiency of predicting scattered fields from a spherical object at arbitrary high frequencies.

The two-body problem of variational electrodynamics possesses differential-delay equations of motion with state-dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets. From a periodic orbit possessing some mild properties at breaking points, we define a synchronization function in R x R3, which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points. The oscillatory functions are associated with a PDE identity in H2(R3), and we postulate ordering conditions for the PDE identity to define a Fredholm-Schroedinger operator with an O(1/r2) spin-orbit forcing term belonging to L2(R3). As an application, we introduce the Chemical Principle criterion to select orbits with asymptotically vanishing far-fields and estimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using the boundary-layer of orbits chosen according to the Chemical Principle criterion. Last, working backward, we derive a Chemical Principle-like condition from the ordering conditions.

In the momentarily comoving frame of a cosmological fluid, the determinant of the energy-momentum tensor (EMT) is highly sensitive to its pressure. This component is significant during radiation-dominated epochs and becomes naturally negligible as the universe transitions to the matter-dominated era. Here, we investigate the cosmological consequences of gravity sourced by the determinant of the EMT. Unlike Azri and Nasri, Phys. Lett. B 836, 137626 (2023), we consider the most general scenario in which the second order variation of the perfect-fluid Lagrangian does not vanish. We analyze the dynamics of the power-law case and explore the cosmological implications of the scale-free model characterized by dimensionless couplings to photons and neutrinos. We show that, unlike various theories based on the EMT, the present setup, which leads to enhanced gravitational effects of radiation (EGER), does not alter the time evolution of the energy density of particle species. Using current cosmological observations, we constrain the model parameters and show that EGER may offer a viable mechanism for alleviating the Hubble tension. Although it exhibits a phenomenological analogy to tightly-coupled relativistic fluid scenarios, EGER remains purely gravitational in origin and yields distinguishable signatures in the small-scale anisotropies of the cosmic microwave background. The radiation-gravity couplings we propose here are expected to yield testable cosmological and astrophysical signatures, probing whether gravity distinguishes between relativistic and nonrelativistic species in the early universe.

The strong coupling between magnetism and ferroelectricity was found in rare earth manganites, where the electric polarization could be induced by special magnetic ordering. There is no theoretical model that would allow us to study the static and dynamic properties of electric polarization in strongly correlated magnetic dielectrics. In the presented research, we have taken the main step towards the construction of such a fundamental model, and made a direct connection between the microscopic Katsura-Nagaosa-Balatsky theory and Mostovoy's phenomenological model for magnetically induced polarization. A novel description of the ferroelectricity of spin origin is proposed within the framework of the many-particle quantum hydrodynamics method. It is applied to the study of cells of magnetic ions, where the electric dipole moment is proportional to the vector product of spins. Our approach is based on the many-particle Pauli equation, where the influence of an external magnetic field is considered. We define the electric dipole moment operator of the ion cell and introduce the macroscopic polarization as the quantum mechanical average of that operator. We formulate a model for the description of nonequilibrium polarization and derive a new polarization evolution equation. The polarization switching in ferroelectric magnets with the spiral spin-density-wave state is considered, and we demonstrate that the proposed model yields known results and can predict novel effects. The dynamic magnetoelectric effect can be investigated by employing this novel equation to study the evolution of polarization.

We investigate properties of holographic strange metals in p+2-dimensions, generalizing the analysis performed in arXiv:0912.1061. The bulk spacetime is p+2-dimensional Lifshitz black hole, while the role of charge carriers is played by probe D-branes. We mainly focus on massless charge carriers, where most of the results can be obtained analytically. We obtain exact results for the free energy and calculate the entropy density, the heat capacity as well as the speed of sound at low temperature. We obtain the DC conductivity and DC Hall conductivity and find that the DC conductivity takes a universal form in the large density limit, while the Hall conductivity is also universal in all dimensions. We also study the resistivity in different limits and clarify the condition for the linear dependence on the temperature, which is a key feature of strange metals. We show that our results for the DC conductivity are consistent with those obtained via Kubo formula and we obtain the charge diffusion constant analytically. The corresponding properties of massive charge carriers are also discussed in brief.

We use the AdS/CFT correspondence to compute the conductivity of massive N=2 hypermultiplet fields at finite baryon number density in an N=4 SU(N_c) super-Yang-Mills theory plasma in the large N_c, large 't Hooft coupling limit. The finite baryon density provides charge carriers analogous to electrons in a metal. An external electric field then induces a finite current which we determine directly. Our result for the conductivity is good for all values of the mass, external field and density, modulo statements about the yet-incomplete phase diagram. In the appropriate limits it agrees with known results obtained from analyzing small fluctuations around equilibrium. For large mass, where we expect a good quasi-particle description, we compute the drag force on the charge carriers and find that the answer is unchanged from the zero density case. Our method easily generalizes to a wide class of systems of probe branes in various backgrounds.

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the U(1) degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous U(1) system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

A cylindrical TM_{0,1,0} mode microwave cavity resonator was excited using a balanced interferometric configuration that allowed manipulation of the electric field and potential within the resonator by adjusting the phase and amplitude of the interferometer arms driving the resonator. With precise tuning of the phase and amplitude, 25 dB suppression of the electric field at the resonance frequency was achieved while simultaneously resonantly enhancing the time-varying electric-scalar potential. Under these conditions, the system demonstrated electromagnetically induced absorption in the cavity response due to the annulment of the electric field at the resonance frequency. This phenomena can be regarded as a form of extreme dispersion, and led to a sharp increase in the cavity phase versus frequency response by an order of magnitude when compared to the cavity Q-factor. This work presents an experimental setup that will allow the electric-scalar Aharonov-Bohm effect to be tested under conditions involving a time-varying electric-scalar potential, without the presence of an electric field or magnetic vector potential, an experiment that has not yet been realised.

We present a theoretical study of the magnetic field generated by a toroidal current loop situated in the equatorial plane of a non-rotating Schwarzschild black hole, based on the dynamics of charged particles. Using the exact general relativistic solution for the magnetic field, we analyze particle motion both analytically and numerically, identifying regions of stable and unstable orbits. In particular, we classify charged particle dynamics into attractive and repulsive Lorentz force configurations and show that in the attractive case, charged particles can accumulate near the current loop, forming collective currents that oppose the original current loop magnetic field. We demonstrate that charged particle accumulation can lead to the formation of toroidal structures analogous to radiation belts in the BH magnetosphere. We compare the curved spacetime solution to flat spacetime analogs and highlight general relativistic effects such as the existence of the innermost stable circular orbit for charged particles, which sets a lower bound for radiation belt formation. The divergence of the vector potential at the loop location in the idealized infinitesimal loop model is addressed, and we argue that a physically realistic model must consider a finite-width current distribution to avoid unphysical divergences in the effective potential.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

We propose a physics-informed neural particle method (PINN--PM) for the spatially homogeneous Landau equation. The method adopts a Lagrangian interacting-particle formulation and jointly parameterizes the time-dependent score and the characteristic flow map with neural networks. Instead of advancing particles through explicit time stepping, the Landau dynamics is enforced via a continuous-time residual defined along particle trajectories. This design removes time-discretization error and yields a mesh-free solver that can be queried at arbitrary times without sequential integration. We establish a rigorous stability analysis in an L^2_v framework. The deviation between learned and exact characteristics is controlled by three interpretable sources: (i) score approximation error, (ii) empirical particle approximation error, and (iii) the physics residual of the neural flow. This trajectory estimate propagates to density reconstruction, where we derive an L^2_v error bound for kernel density estimators combining classical bias--variance terms with a trajectory-induced contribution. Using Hyvarinen's identity, we further relate the oracle score-matching gap to the L^2_v score error and show that the empirical loss concentrates at the Monte Carlo rate, yielding computable a posteriori accuracy certificates. Numerical experiments on analytical benchmarks, including the two- and three-dimensional BKW solutions, as well as reference-free configurations, demonstrate stable transport, preservation of macroscopic invariants, and competitive or improved accuracy compared with time-stepping score-based particle and blob methods while using significantly fewer particles.

In this work, we propose an effective action of the two-dimensional conformal field theory for the Soft modes appearing in Quantum ElectroDynamics (QED) in 4 dimensions. This is motivated in two ways. First, we motivate the notion of an effective action for the Soft modes using the path integral formalism. Second, by noting the transformations of the on-shell gauge-fixed QED action, we deduce necessary boundary conditions and the corresponding form of the counter-terms that govern the IR sector. We review a derivation of the Soft Ward-Takahashi identity using path integral methods and offer an alternative derivation that follows from the large-gauge variations of the QED action. Because our effective action is that of a conformal theory, we calculate the relevant central charge.

We introduce a neural network (NN) strictly governed by Newton's Law, with the nature required basis functions derived from the fundamental classic mechanics. Then, by classifying the training model as a quick procedure of 'force pattern' recognition, we developed the Newton physics-based NS scheme. Once the force pattern is confirmed, the neuro network simply does the checking of the 'pattern stability' instead of the continuous fitting by computational resource consuming big data-driven processing. In the given physics's law system, once the field is confirmed, the mathematics bases for the force field description actually are not diverged but denumerable, which can save the function representations from the exhaustible available mathematics bases. In this work, we endorsed Newton's Law into the deep learning technology and proposed Newton Scheme (NS). Under NS, the user first identifies the path pattern, like the constant acceleration movement.The object recognition technology first loads mass information, then, the NS finds the matched physical pattern and describe and predict the trajectory of the movements with nearly zero error. We compare the major contribution of this NS with the TCN, GRU and other physics inspired 'FIND-PDE' methods to demonstrate fundamental and extended applications of how the NS works for the free-falling, pendulum and curve soccer balls.The NS methodology provides more opportunity for the future deep learning advances.

Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability (MRI) as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi&Pharr, ApJ 2022), confined either between two Alfv\'enic resonances or an Alfv\'enic resonance and a boundary.

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p, q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces R^{p,q}. They cover, for instance, E(3)-equivariance on R^3 and Poincaré-equivariance on Minkowski spacetime R^{1,3}. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

How momentum, energy, and magnetic fields are transported in the presence of macroscopic gradients is a fundamental question in plasma physics. Answering this question is especially challenging for weakly collisional, magnetized plasmas, where macroscopic gradients influence the plasma's microphysical structure. In this paper, we introduce thermodynamic forcing, a new method for systematically modeling how macroscopic gradients in magnetized or unmagnetized plasmas shape the distribution functions of constituent particles. In this method, we propose to apply an anomalous force to those particles inducing the anisotropy that would naturally emerge due to macroscopic gradients in weakly collisional plasmas. We implement thermodynamic forcing in particle-in-cell (TF-PIC) simulations using a modified Vay particle pusher and validate it against analytic solutions of the equations of motion. We then carry out a series of simulations of electron-proton plasmas with periodic boundary conditions using TF-PIC. First, we confirm that the properties of two electron-scale kinetic instabilities -- one driven by a temperature gradient and the other by pressure anisotropy -- are consistent with previous results. Then, we demonstrate that in the presence of multiple macroscopic gradients, the saturated state can differ significantly from current expectations. This work enables, for the first time, systematic and self-consistent transport modeling in weakly collisional plasmas, with broad applications in astrophysics, laser-plasma physics, and inertial confinement fusion.

Recently, machine learning Hamiltonian (MLH) models have gained traction as fast approximations of electronic structures such as orbitals and electron densities, while also enabling direct evaluation of energies and forces from their predictions. However, despite their physical grounding, existing Hamiltonian models are evaluated mainly by reconstruction metrics, leaving it unclear how well they perform as energy-force predictors. We address this gap with a benchmark that computes energies and forces directly from predicted Hamiltonians. Within this framework, we propose QHFlow2, a state-of-the-art Hamiltonian model with an SO(2)-equivariant backbone and a two-stage edge update. QHFlow2 achieves 40% lower Hamiltonian error than the previous best model with fewer parameters. Under direct evaluation on MD17/rMD17, it is the first Hamiltonian model to reach NequIP-level force accuracy while achieving up to 20times lower energy MAE. On QH9, QHFlow2 reduces energy error by up to 20times compared to MACE. Finally, we demonstrate that QHFlow2 exhibits consistent scaling behavior with respect to model capacity and data, and that improvements in Hamiltonian accuracy effectively translate into more accurate energy and force computations.

In the present paper we study the singularity structure of the exterior field of neutron stars with the aid of the four-parameter exact solution of the Einstein-Maxwell equations. The complete analysis of this problem in the generic case becomes possible due to the implementation of the novel analytical approach to the resolution of the singularity condition, and it shows the absence of the ring singularities off the symmetry axis in the positive mass case, as well as the possibility of the removal of the ring singularity by a strong magnetic field in the negative mass case. The solution takes an extraordinarily simple form in the equatorial plane, very similar to that of the Kerr solution, which makes it most suitable for astrophysical applications as the simplest model of a rotating magnetized deformed mass. It also provides a nontrivial example confirming a recent claim that the varphi component of the electromagnetic four-potential has features inconsistent with the intrinsic properties of the electrovac metric, while the magnetic field is represented correctly by the t component of the dual electromagnetic four-potential.

Although Maxwell discovered the physical laws of electromagnetic waves 160 years ago, how to precisely model the propagation of an RF signal in an electrically large and complex environment remains a long-standing problem. The difficulty is in the complex interactions between the RF signal and the obstacles (e.g., reflection, diffraction, etc.). Inspired by the great success of using a neural network to describe the optical field in computer vision, we propose a neural radio-frequency radiance field, NeRF^2, which represents a continuous volumetric scene function that makes sense of an RF signal's propagation. Particularly, after training with a few signal measurements, NeRF^2 can tell how/what signal is received at any position when it knows the position of a transmitter. As a physical-layer neural network, NeRF^2 can take advantage of the learned statistic model plus the physical model of ray tracing to generate a synthetic dataset that meets the training demands of application-layer artificial neural networks (ANNs). Thus, we can boost the performance of ANNs by the proposed turbo-learning, which mixes the true and synthetic datasets to intensify the training. Our experiment results show that turbo-learning can enhance performance with an approximate 50% increase. We also demonstrate the power of NeRF^2 in the field of indoor localization and 5G MIMO.

The KMOC formalism provides a systematic framework for extracting classical observables perturbatively from on-shell scattering amplitudes. In this work, we apply this formalism to compute electromagnetic observables in four dimensions, focusing in particular on the linear memory effect and its tail contributions. Using the leading and subleading soft-photon theorems to construct the soft radiation kernel, we demonstrate how these infrared observables emerge directly from amplitude data. We further show that demanding the expected non-perturbative properties of memory and tail effects imposes a nontrivial set of consistency conditions on the underlying S-matrix. We interpret these constraints as imposing the requirement of macroscopic causality on the S-matrix via analysis of inclusive observables.

The classical Coulomb gas model has served as one of the most versatile frameworks in statistical physics, connecting a vast range of phenomena across many different areas. Nonequilibrium generalisations of this model have so far been studied much more scarcely. With the abundance of contemporary research into active and driven systems, one would naturally expect that such generalisations of systems with long-ranged Coulomb-like interactions will form a fertile playground for interesting developments. Here, we present two examples of novel macroscopic behaviour that arise from nonequilibrium fluctuations in long-range interacting systems, namely (1) unscreened long-ranged correlations in strong electrolytes driven by an external electric field and the associated fluctuation-induced forces in the confined Casimir geometry, and (2) out-of-equilibrium critical behaviour in self-chemotactic models that incorporate the particle polarity in the chemotactic response of the cells. Both of these systems have nonlocal Coulomb-like interactions among their constituent particles, namely, the electrostatic interactions in the case of the driven electrolyte, and the chemotactic forces mediated by fast-diffusing signals in the case of self-chemotactic systems. The results presented here hint to the rich phenomenology of nonequilibrium effects that can arise from strong fluctuations in Coulomb interacting systems, and a rich variety of potential future directions, which are discussed.

A universal class of light-ray operators formed from null integrals of the stress tensor is constructed in generic interacting Lorentzian conformal field theories in four spacetime dimensions. This class of light-ray operators generates the wedge algebra of {rm w}_{1+infty}, which was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. In four-dimensional conformal field theories with an additional spin-one conserved current, a second universal class of light-ray operators is constructed and shown to generate the ''S algebra,'' the gauge-theoretic analog of {rm w}_{1+infty}. Finally, a precise relation is established between the one-point functions of these light-ray operators in scalar states and the universal soft factors in the infinite tower of soft graviton theorems. The results presented in this paper will be accompanied by detailed calculations and proofs in a longer forthcoming work.

The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator p_t = q_t - q_{t-1}, implementing the symplectic shear q_t = q_t + γp_t on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint (L geq 2) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within sim2.9% validation loss. Dedicated associative recall experiments reveal a scaling law γ^* = 4.17 times N^{-0.74} establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.

We introduce a dark photon considering a U(1) gauge extension of the standard model in particle physics. Provided that the extra U(1) symmetry is unbroken, the dark photon is massless and has no coupling to the standard electromagnetic current. Higher-dimensional operators describe interactions of the massless dark photon with particles in the standard model. We investigate the interactions of the massless dark photon with charged leptons via dipole operators, mainly focusing on the lepton family-violating processes. We present an improved constraint in the polarized two-body muon decay and a set of new bounds in tau decays. We also examine possible lepton family-violating signals of the massless dark photon in future lepton colliders.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

Nonreciprocal circuit elements form an integral part of modern measurement and communication systems. Mathematically they require breaking of time-reversal symmetry, typically achieved using magnetic materials and more recently using the quantum Hall effect, parametric permittivity modulation or Josephson nonlinearities. Here, we demonstrate an on-chip magnetic-free circulator based on reservoir engineered optomechanical interactions. Directional circulation is achieved with controlled phase-sensitive interference of six distinct electro-mechanical signal conversion paths. The presented circulator is compact, its silicon-on-insulator platform is compatible with both superconducting qubits and silicon photonics, and its noise performance is close to the quantum limit. With a high dynamic range, a tunable bandwidth of up to 30 MHz and an in-situ reconfigurability as beam splitter or wavelength converter, it could pave the way for superconducting qubit processors with integrated and multiplexed on-chip signal processing and readout.

Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered are Ca^{2+} waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A on Ca^{2+} momentum, p. The canonical momentum of a charged particle in an electromagnetic field, mathbfΠ = p + q A (SI units), is calculated, where the charge of Ca^{2+} is q = - 2 e, e is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG A can be quite influential on the momentum p of Ca^{2+} ions, in both classical and quantum mechanics. Molecular scales of Ca^{2+} wave dynamics are coupled with A fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting A models to EEG data as reported here, building tripartite models to develop A models, and studying long coherence times of Ca^{2+} waves in the presence of A due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the p + q A interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.

We investigate the stability of superconducting strings as bound states of strings and fermion zero modes at both the classical and quantum levels. The dynamics of these superconducting strings can result in a stable configuration, known as a vorton. We mainly focus on global strings, but the majority of the discussion can be applied to local strings. Using lattice simulations, we study the classical dynamics of superconducting strings and confirm that they relax to the vorton configuration through Nambu-Goldstone boson radiation, with no evidence of over-shooting that would destabilize the vorton. We explore the tunneling of fermion zero modes out of the strings. Both our classical analysis and quantum calculations yield consistent results: the maximum energy of the zero mode significantly exceeds the fermion mass, in contrast to previous literature. Additionally, we introduce a world-sheet formalism to evaluate the decay rate of zero modes into other particles, which constitute the dominant decay channel. We also identify additional processes that trigger zero-mode decay due to non-adiabatic changes of the string configuration. In these decay processes, the rates are suppressed by the curvature of string loops, with exponential suppression for large masses of the final states. We further study the scattering with light charged particles surrounding the string core produced by the zero-mode current and find that a wide zero-mode wavefunction can enhance vorton stability.

We use two-dimensional particle-in-cell simulations to investigate the generation and evolution of the magnetic field associated with the propagation of a jet for various initial conditions. We demonstrate that, in general, the magnetic field is initially grown by the Weibel and Mushroom instabilities. However, the field is saturated by the Alfv'en current limit. For initially non-magnetized plasma, we show that the growth of the magnetic field is delayed when the matter density of the jet environment is lower, which are in agreement with simple analytical predictions. We show that the higher Lorentz factor (gtrsim 2) prevents rapid growth of the magnetic fields. When the initial field is troidal, the position of the magnetic filaments moves away from the jet as the field strength increases. The axial initial field helps the jet maintain its shape more effectively than the troidal initial field.

One way to model the strange metal phase of certain materials is via a holographic description in terms of probe D-branes in a Lifshitz spacetime, characterised by a dynamical exponent z. The background geometry is dual to a strongly-interacting quantum critical theory while the probe D-branes are dual to a finite density of charge carriers that can exhibit the characteristic properties of strange metals. We compute holographically the low-frequency and low-momentum form of the charge density and current retarded Green's functions in these systems for massless charge carriers. The results reveal a quasi-particle excitation when z<2, which in analogy with Landau Fermi liquids we call zero sound. The real part of the dispersion relation depends on momentum k linearly, while the imaginary part goes as k^2/z. When z is greater than or equal to 2 the zero sound is not a well-defined quasi-particle. We also compute the frequency-dependent conductivity in arbitrary spacetime dimensions. Using that as a measure of the charge current spectral function, we find that the zero sound appears only when the spectral function consists of a single delta function at zero frequency.

Elemental abundances in the solar corona differ from those in the photosphere, with low first ionization potential (FIP) elements being enhanced, a phenomenon known as the FIP effect. This enhancement is attributed to ponderomotive forces linked to magnetohydrodynamic (MHD) waves, particularly incompressible transverse waves. Our study investigates the relationship between coronal abundance fractionation and chromospheric transverse MHD waves by examining the spatial correlation between FIP fractionation and these waves and by analyzing their properties to test the ponderomotive force model. We used H alpha data from the Fast Imaging Solar Spectrograph at the Goode Solar Telescope to detect chromospheric transverse MHD waves and Si{X} (low FIP) and S{X} (high FIP) spectra from Hinode EUV Imaging Spectrometer to determine relative abundances in an active region. Extrapolated linear force free magnetic fields from Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetograms further linked the observed chromospheric waves with coronal composition. Approximately 400 wave packets were identified and characterized by their period, velocity amplitude, propagation speed, and direction. These incompressible or weakly compressible waves were mainly observed near loop footpoints in the sunspot penumbra and superpenumbral fibrils. Regions of high FIP fractionation coincided with closed magnetic fields where these waves were present, and low-frequency, downward-propagating waves comprised about 43/% of the total. Our results demonstrate a strong correlation between coronal abundance fractionation and chromospheric transverse MHD waves, supporting the view that the FIP effect is driven by the ponderomotive force from these waves.

Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. Particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to magnetic field can play an important, if not dominant role. In this study, we carry out 2D fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameter sigma_0=20, we find that the injection energy {varepsilon}_{rm inj} converges with increasing domain size to {varepsilon}_{rm inj}simeq 10m_ec^2. In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel (W_parallel) and perpendicular (W_perp) electric fields during both the injection phase and the post-injection phase. We find that during the injection phase, the W_perp contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, both components contribute equally during the post-injection phase, insensitive to the domain size. For high energy ({varepsilon}varepsilon_{rm inj}) particles, W_perp dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

We perform a lattice QCD calculation of the hadronic light-by-light contribution to (g-2)_μ at the SU(3) flavor-symmetric point m_π=m_Ksimeq 420,MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain a_μ^{rm hlbl} = (65.4pm 4.9 pm 6.6)times 10^{-11}, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

We present a complete Lean 4 formalization of the equilibrium characterization in the Vlasov-Maxwell-Landau (VML) system, which describes the motion of charged plasma. The project demonstrates the full AI-assisted mathematical research loop: an AI reasoning model (Gemini DeepThink) generated the proof from a conjecture, an agentic coding tool (Claude Code) translated it into Lean from natural-language prompts, a specialized prover (Aristotle) closed 111 lemmas, and the Lean kernel verified the result. A single mathematician supervised the process over 10 days at a cost of \$200, writing zero lines of code. The entire development process is public: all 229 human prompts, and 213 git commits are archived in the repository. We report detailed lessons on AI failure modes -- hypothesis creep, definition-alignment bugs, agent avoidance behaviors -- and on what worked: the abstract/concrete proof split, adversarial self-review, and the critical role of human review of key definitions and theorem statements. Notably, the formalization was completed before the final draft of the corresponding math paper was finished.

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function varepsilon(z,z) on the conformal sphere at future null infinity (mathscr I^+) but are independent of the retarded time. The value of varepsilon at past null infinity (mathscr I^-) is determined from that on mathscr I^+ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The varepsilonneq constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

The Numerical Flow Iteration (NuFI) method has recently been proposed as a memory-slim solution method for the Vlasov--Poisson system. It stores the temporal evolution of the electric field, instead of the distribution functions, and reconstructs the solution in each time step by following the characteristics backwards in time and reconstructing the solution from the initial distribution. NuFI has been shown to be more accurate than other state-of-the-art Vlasov solvers given the same amount of degrees of freedom as well as interpolation order, essentially making NuFI a high-fidelity but low-memory cost scheme. In this paper, we build on the Hamiltonian structure of the full Vlasov--Maxwell system to extend NuFI to handle electro-magnetic kinetic plasma dynamics. We show that the advanced structure-preserving properties of NuFI are preserved when extending to the electro-magnetic case.

Within the paradigm of metamaterials and metasurfaces, electromagnetic properties of composite materials can be engineered by shaping or modulating their constituents, so-called meta-atoms. Synthesis and analysis of complex-shape meta-atoms with general polarization properties is a challenging task. In this paper, we demonstrate that the most general response can be conceptually decomposed into a set of basic, fundamental polarization phenomena, which enables immediate all-direction characterization of electromagnetic properties of arbitrary linear metamaterials and metasurfaces. The proposed platform of modular characterization (called "materiatronics") is tested on several examples of bianisotropic and nonreciprocal meta-atoms. As a demonstration of the potential of the modular analysis, we use it to design a single-layer metasurface of vanishing thickness with unitary circular dichroism. The analysis approach developed in this paper is supported by a ready-to-use computational code and can be further extended to meta-atoms engineered for other types of wave interactions, such as acoustics and mechanics.

Reduction in effective spacetime dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wavefunction factors depend nontrivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a "covert" pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.

We investigate the thermodynamic and hydrodynamic properties of 4-dimensional gauge theories with finite electric charge density in the presence of a constant magnetic field. Their gravity duals are planar magnetically and electrically charged AdS black holes in theories that contain a gauge Chern-Simons term. We present a careful analysis of the near horizon geometry of these black branes at finite and zero temperature for the case of a scalar field non-minimally coupled to the electromagnetic field. With the knowledge of the near horizon data, we obtain analytic expressions for the shear viscosity coefficient and entropy density, and also study the effect of a generic set of four derivative interactions on their ratio. We also comment on the attractor flows of the extremal solutions.

We study the S-matrix and inclusive cross-section for general dressed states in quantum electrodynamics. We obtain an infrared factorization formula of the S-matrix elements for general dressed states. It enables us to study what dressed states lead to infrared-safe S-matrix elements. The condition for dressed states can be interpreted as the memory effect which is nothing but the conservation law of the asymptotic symmetry. We derive the generalized soft photon theorem for general dressed states. We also compute inclusive cross-section using general dressed states. It is necessary to use appropriate initial and final dressed states to evaluate interference effects, which cannot be computed correctly by using Fock states due to the infrared divergence.

Cavity quantum electrodynamics has been studied as a potential approach to modify free charge carrier generation in donor-acceptor heterojunctions because of the delocalization and controllable energy level properties of hybridized light-matter states known as polaritons. However, in many experimental systems, cavity coupling decreases charge separation. Here, we theoretically study the quantum dynamics of a coherent and dissipative donor-acceptor cavity system, to investigate the dynamical mechanism and further discover the conditions under which polaritons may enhance free charge carrier generation. We use open quantum system methods based on single-pulse pumping to find that polaritons have the potential to connect excitonic states and charge separated states, further enhancing free charge generation on an ultrafast timescale of several hundred femtoseconds. The mechanism involves that polaritons with proper energy levels allow the exciton to overcome the high Coulomb barrier induced by electron-hole attraction. Moreover, we propose that a second-hybridization between a polariton state and dark states with similar energy enables the formation of the hybrid charge separated states that are optically active. These two mechanisms lead to a maximum of 50% enhancement of free charge carrier generation on a short timescale. However, our simulation reveals that on the longer timescale of picoseconds, internal conversion and cavity loss dominate and suppress free charge carrier generation, reproducing the experimental results. Thus, our work shows that polaritons can affect the charge separation mechanism and promote free charge carrier generation efficiency, but predominantly on a short timescale after photoexcitation.

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

We introduce a platform to achieve ultra-strong coupling (USC) between light and matter using widely available materials. USC is a light-matter interaction regime characterized by coupling strengths exceeding 10% of the ground state energy. It gives rise to novel physical phenomena, such as efficient single-photon coupling and quantum gates, with applications in quantum sensing, nonlinear optics, and low-threshold lasing. Although early demonstrations in plasmonic systems have been realized, achieving USC in dielectric platforms, which offer lower losses and high Q-factors, remains challenging due to typically low mode overlap between the photonic field and the material resonance. Here we leverage dielectric dual gradient metasurfaces supporting quasi-bound states in the continuum to spatially encode both the spectral and coupling parameter space and demonstrate USC to an epsilon-near-zero (ENZ) mode in an ultra-thin SiO2 layer. The strong out-of-plane electric fields in our tapered bar structure overlap exceptionally well with those of the ENZ mode, resulting in a normalized coupling strength of 0.101 and a mode splitting equivalent to 20% of the ENZ mode energy; a four- to five-fold increase compared to previous approaches. The strong field confinement of our approach opens new possibilities for compact and scalable polaritonic devices, such as tunable frequency converters and low-energy optical modulators.

In detuned optical cavities, the radiation pressure force acting on the mirrors depends on their displacements. This is equivalent to the rigidity (the optical spring), inserted between the mirrors. This effect can be used for optimization of the mechanical susceptibility of probe mirrors in high-precision force sensors. However, in some cases, the use of detuned cavities or even just any high-finesse cavities could be problematic due to technological constraints. We consider a new type of the optical spring that does not require the cavity (but can use a resonance tuned one to increase the optomechanical coupling). Instead, it uses the double interaction of the probing light with the mechanical object. We propose two possible implementation of this concept, suitable, respectively, for the atomic spin ensembles and for the laser gravitational-wave detectors.

We continue our analysis on conductivity in the anisotropic background by employing the D-brane probe technique, where the D-branes play the role of charge carriers. The DC and AC conductivity for massless charge carriers are obtained analytically, while interesting curves for the AC conductivity are also plotted. For massive charge carriers, we calculate the DC and AC conductivities in the dilute limit and we fix the parameters in the Einstein-Maxwell-dilaton theory so that the background exhibits the same scaling behaviors as those for real-world strange metals. The DC conductivity at finite density is also computed.

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, Wavelet, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.

Quantum liquids are characterized by the distinctive properties such as the low temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by L. D. Landau in 1957 and subsequently observed in liquid He-3. In this paper, we ask a question whether such a characteristic behavior is present in theories with holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in AdS_{p+1} space. An example of such a system is the N=4 SU(N_c) supersymmetric Yang-Mills theory with N_f massless N=2 hypermultiplets at strong coupling, finite baryon number density, and low temperature. We find that these systems exhibit a zero sound mode despite having a non-Fermi liquid type behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquids.

We describe the first-principles design and subsequent synthesis of a new material with the specific functionalities required for a solid-state-based search for the permanent electric dipole moment of the electron. We show computationally that perovskite-structure europium barium titanate should exhibit the required large and pressure-dependent ferroelectric polarization, local magnetic moments, and absence of magnetic ordering even at liquid helium temperature. Subsequent synthesis and characterization of Eu_{0.5}Ba_{0.5}TiO_3 ceramics confirm the predicted desirable properties.

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the H\'enon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.

Fuzzy (wave) dark matter (FDM), the dynamical model underlying an ultralight bosonic dark matter species, produces a rich set of non-gravitational signatures that distinguishes it markedly from the phenomenologically related warm (particle) dark matter (WDM) scenario. The emergence of extended interference fringes hosted by cosmic filaments is one such phenomenon reported by cosmological simulations, and a detailed understanding of such may strengthen existing limits on the boson mass but also break the degeneracy with WDM, and provide a unique fingerprint of interference in cosmology. In this paper, we provide initial steps towards this goal. In particular, we show in a bottom-up approach, how the presence of interference in an idealised filament population can lead to a non-suppressive feature in the matter power spectrum -- an observation supported by fully-cosmological FDM simulations. To this end, we build on a theoretically motivated and numerically observed steady-state approximation for filaments and express the equilibrium dynamics of such in an expansion of FDM eigenstates. We optimise the size of the expansion by incorporating classical phase-space information. Ellipsoidal collapse considerations are used to construct a fuzzy filament mass function which, together with the reconstructed FDM wave function, allow us to efficiently compute the one-filament power spectrum. We showcase our non-perturbative interference model for a selection of boson masses and confirm our approach is able to produce the matter power boost observed in fully-cosmological FDM simulations. More precisely, we find an excess in correlation between the spatial scale associated with the FDM ground state and the quantum pressure scale. We speculate about applications of this effect in data analysis.

We evaluate electromagnetic-response observables in a half-filled Chern band, across a topological phase transition between a composite Fermi liquid (CFL) and a Fermi liquid (FL) phase. While a sharp gapped plasma mode exists deep in the CFL phase, we demonstrate that it is damped near the proposed continuous phase transition between CFL and FL. This plasmon-damping phenomenon originates from emergent gauge fields and a Dirac-fermion-like spectrum. Similar features also occur in other continuous deconfined topological phase transitions, such as the Laughlin to superfluid transition in a bosonic system. In particular, this damping behavior extends over a finite range across the phase boundary, and, hence, we expect it to persist even when the transition is weakly first-order. Furthermore, we analyze the behavior of the Drude weight, the wavevector-dependent conductivity, and the chiral mirror effect across these topological phase transitions.

An experimental demonstration of directivities exceeding the fundamental Kildal limit, a phenomenon called superdirectivity, is provided for spherical high-index dielectric antennas with an electric dipole excitation. A directivity factor of about 10 with a total efficiency of more than 80\% for an antenna having a size of a third of the wavelength was measured. High directivities are shown to be associated with constructive interference of particular electric and magnetic modes of an open spherical resonator. Both analytic solution for a point dipole and a full-wave rigorous simulation for a realistic dipole antenna were employed for optimization and analysis, yielding an excellent agreement between experimentally measured and numerically predicted directivities. The use of high-index low-loss ceramics can significantly reduce the physical size of such antennas while maintaining their overall high radiation efficiency. Such antennas can be attractive for various high-frequency applications, such as antennas for the Internet of things, smart city systems, 5G network systems, and others. The demonstrated concept can be scaled in frequency.

We verify a recent prediction (Eq. 3.50 in G. L. Eyink, Phys. Rev. X 11, 031054 (2021)) for the drag on an object moving through a fluid. In this prediction the velocity field is decomposed into a nonvortical (potential) and vortical contribution, and so is the associated drag force. In the Josephson-Anderson relation the vortical contribution of the drag force follows from the flux of vorticity traversing the streamlines of the corresponding potential flow. The potential component is directly determined by the plate acceleration and its added mass. The Josephson-Anderson relation is derived from the quantum description of superfluids, but remarkably applies to the classical fluid in our experiment. In our experiment a flat plate is accelerated through water using a robotic arm. This geometry is simple enough to allow analytic potential flow streamlines. The monitored plate position shows an oscillatory component of the acceleration, which adds an additional test of the Josephson-Anderson relation. The instantaneous velocity field is measured using particle image velocimetry. It enables us to evaluate Eq. 3.50 from [1] and compare its prediction to the measured drag force. We find excellent agreement, and, most remarkably find that the added mass contribution to the drag force still stands out after the flow has turned vortical. We finally comment on the requirements on the experimental techniques for evaluating the Josephson-Anderson relation.

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semi-circle transitions between them. The model can be regarded as a strongly coupled analog of the old `composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model.

Plasma modeling is central to the design of nuclear fusion reactors, yet simulating collisional plasma kinetics from first principles remains a formidable computational challenge: the Vlasov-Maxwell-Landau (VML) system describes six-dimensional phase-space transport under self-consistent electromagnetic fields together with the nonlinear, nonlocal Landau collision operator. A recent deterministic particle method for the full VML system estimates the velocity score function via the blob method, a kernel-based approximation with O(n^2) cost. In this work, we replace the blob score estimator with score-based transport modeling (SBTM), in which a neural network is trained on-the-fly via implicit score matching at O(n) cost. We prove that the approximated collision operator preserves momentum and kinetic energy, and dissipates an estimated entropy. We also characterize the unique global steady state of the VML system and its electrostatic reduction, providing the ground truth for numerical validation. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is more accurate than the blob method, achieves correct long-time relaxation to Maxwellian equilibrium where the blob method fails, and delivers 50% faster runtime with 4times lower peak memory.

Spontaneous symmetry breaking is examined by regarding it as a phenomenon in the eternal intermediate state due to sequential perturbations. The concept of the relativistic many-body state is applied to this intermediate state occurring in the collision of massless Dirac fermions. Time in the relativistic many-body state should evolve while maintaining the direction of time in each particle, even if the particles are viewed from any inertial frames. This kinematical requirement leads to spontaneous symmetry breaking in the vacuum of these states, which gives a different meaning to the results of the Higgs model. In this vacuum, massless fermion-antifermion pairs and coherent collection of gauge bosons condense, which determine each other's mass. When a local excitation of the condensed gauge bosons propagates in space, a Higgs-like boson appears. The effective coupling of this Higgs-like boson to gauge bosons is calculated as a one-loop process. With this coupling, the total cross section of the pair annihilation of fermion and antifermion to gauge boson pair is calculated. Renormalizability of this model is discussed using the inductive method. Since the Higgs Lagrangian is not assumed, the divergence we must renormalize is only the logarithmic divergence, not the quadratic one.

We propose a mass-dependent MOM scheme to renormalize UV divergence of unpolarized PDFs at one-loop order. This approach which is based on a once subtracted dispersion relation does not need any regulator. The overall counterterms are obtained from the imaginary part of large transverse momentum region in loop integrals. The mass-dependent characteristic of the scheme yields to mass-dependent splitting functions for the DGLAP evolution equations. While the flavor number is fixed at any renormalization scale, the decoupling theorem is automatically imposed by the mass-dependent splitting functions. The required symmetries are also automatically respected by our prescription.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of condensed-matter lattice models with coupled electronic and structural or magnetic degrees of freedom. However, most existing formulations rely on hand-crafted, symmetry-aware descriptors, whose construction is often system-specific and can hinder generality and transferability across different lattice Hamiltonians. Here we introduce a symmetry-preserving framework based on equivariant neural networks (ENNs) that provides a general, data-driven mapping from local configurations of dynamical variables to the associated on-site forces in a lattice Hamiltonian. In contrast to ENN architectures developed for molecular systems -- where continuous Euclidean symmetries dominate -- our approach aims to embed the discrete point-group and internal symmetries intrinsic to lattice models directly into the neural-network representation of the force field. As a proof of principle, we construct an ENN-based force-field model for the adiabatic dynamics of the Holstein Hamiltonian on a square lattice, a canonical system for electron-lattice physics. The resulting ML-enabled large-scale dynamical simulations faithfully capture mesoscale evolution of the symmetry-breaking phase, illustrating the utility of lattice-equivariant architectures for linking microscopic electronic processes to emergent dynamical behavior in condensed-matter lattice systems.

Foundation models have revolutionized natural language processing through a ``train once, deploy anywhere'' paradigm, where a single pre-trained model adapts to countless downstream tasks without retraining. Access to a Physics Foundation Model (PFM) would be transformative -- democratizing access to high-fidelity simulations, accelerating scientific discovery, and eliminating the need for specialized solver development. Yet current physics-aware machine learning approaches remain fundamentally limited to single, narrow domains and require retraining for each new system. We present the General Physics Transformer (GPhyT), trained on 1.8 TB of diverse simulation data, that demonstrates foundation model capabilities are achievable for physics. Our key insight is that transformers can learn to infer governing dynamics from context, enabling a single model to simulate fluid-solid interactions, shock waves, thermal convection, and multi-phase dynamics without being told the underlying equations. GPhyT achieves three critical breakthroughs: (1) superior performance across multiple physics domains, outperforming specialized architectures by up to 29x, (2) zero-shot generalization to entirely unseen physical systems through in-context learning, and (3) stable long-term predictions through 50-timestep rollouts. By establishing that a single model can learn generalizable physical principles from data alone, this work opens the path toward a universal PFM that could transform computational science and engineering.

It is demonstrated that self-diffusion and shear viscosity data for the TIP4P/Ice water model reported recently [L. Baran, W. Rzysko and L. MacDowell, J. Chem. Phys. {\bf 158}, 064503 (2023)] obey the microscopic version of the Stokes-Einstein relation without the hydrodynamic diameter.

For a real quadratic field Q(d), we study the norm-form energy N = S_ζ^2 - d cdot S_L^2, where S_ζ and S_L are Lorentzian-weighted zero sums with w(ρ) = 2/(1/4 + γ^2). We prove three main results. (1) Spacelike spectral data: N < 0 unconditionally for all squarefree d > 1, as a consequence of a low-lying zero dominance theorem proved via explicit zero-counting. (2) Effective density bound: at each verified truncation level M, dens{N > 0} leq 2|f_{S_L^{(M)}}|_infty cdot (W_1(ζ)/d + ε_M), established unconditionally via Jacobi--Anger resonance analysis. (3) Exact asymptotic: under the computationally verified hypothesis that the infinite resonance lattice Λ_infty has finite rank (verified for M leq 20, where rank = 0), the sharp asymptotic dens{N > 0} = C(d)/d + o(1/d) holds. For d = 5, C(5) = 2,f_{S_L}(0)cdotE[|S_ζ|] = 0.1191; the constant depends on d through the zeros of L(s,χ_d), and C(d) = O(1/log d) as d to infty.

Reciprocity is a fundamental symmetry present in many natural phenomena and engineered systems. Distinct situations where this symmetry is broken are typically grouped under the umbrella term "nonreciprocity", colloquially defined by: the action of A on B neq the action of B on A. In this review, we elucidate what nonreciprocity is by providing an introduction to its most salient classes: nonvariational dynamics, violations of Newton's third law, broken detailed balance, nonreciprocal responses and nonreciprocity of arbitrary linear operators. Next, we point out where to find these manifestations of non-reciprocity, from ensembles of particles with field mediated interactions to synthetic neural networks and open quantum systems. Given this breadth of contexts and the lack of an all-encompassing definition, it makes it all the more intriguing that some general conclusions can be gathered, when distinct definitions of nonreciprocity overlap. We explore what these universal consequences are with a special emphasis on collective phenomena that arise in nonreciprocal many-body systems. The topics covered include nonreciprocal phase transitions and non-normal amplification of noise and perturbations. We conclude with some open questions.

In this paper, we consider the stability of the Lamb dipole solution of the two-dimensional Euler equations in R^{2} and question under which initial disturbance the Lamb dipole is stable, motivated by experimental work on the formation of a large vortex dipole in two-dimensional turbulence. We assume (O) odd symmetry for the x_2-variable and (N) non-negativity in the upper half plane for the initial disturbance of vorticity, and establish the stability theorem of the Lamb dipole without assuming (F) finite mass condition. The proof is based on a new variational characterization of the Lamb dipole using an improved energy inequality.

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free framework that removes this bottleneck completely. We decouple basis discovery from the solving process. We meta-train a dual-branch neural network on diverse Gaussian Random Fields. This offline process creates a universal dictionary of neural basis functions. At test time, we freeze the network. We solve the PDE by assembling a collocation matrix. We find the solution through a single linear least squares step. For non-linear PDEs, we apply the Newton-Raphson method to achieve fast quadratic convergence. Our experiments across six 2D and 3D PDEs show massive improvements. MetaColloc reaches state-of-the-art accuracy on smooth and non-linear problems. It also reduces test-time computation by several orders of magnitude. Finally, we provide a detailed frequency sweep analysis. This analysis reveals a critical mismatch between function approximation and operator stability at extremely high frequencies. This profound finding opens a clear path toward future operator-aware meta-learning.

We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when z geq 2. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.

In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory and operator splitting, we derive a principled operator-level decomposition. The result is a Hybrid Eulerian-Lagrangian architecture with an algebraic-level inductive bias we call Hodge Spectral Duality (HSD). In our framework, we use discrete differential forms to capture topology-dominated components and an orthogonal auxiliary ambient space to represent complex local dynamics. Our method achieves superior accuracy and efficiency on geometric graphs with enhanced fidelity to physical invariants. Our code is available at https://github.com/ContinuumCoder/Hodge-Spectral-Duality

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from the target PDE, they often overlook more fundamental physical principles underlying these equations. Inspired by how numerical solvers are compatible with simulations of different settings of PDEs, we propose a multiphysics training framework that jointly learns from both the original PDEs and their simplified basic forms. Our framework enhances data efficiency, reduces predictive errors, and improves out-of-distribution (OOD) generalization, particularly in scenarios involving shifts of physical parameters and synthetic-to-real transfer. Our method is architecture-agnostic and demonstrates consistent improvements in normalized root mean square error (nRMSE) across a wide range of 1D/2D/3D PDE problems. Through extensive experiments, we show that explicit incorporation of fundamental physics knowledge significantly strengthens the generalization ability of neural operators. We will release models and codes at https://sites.google.com/view/sciml-fundemental-pde.

Subwavelength atomic lattices have emerged as a promising platform for quantum applications, leveraging collective superradiant and subradiant effects to enhance light-matter interactions. Integrating atomic lattices into nanostructures is at the front of effort toward any application with atomic lattices, but is still a challenging theoretical task, as the dipole interactions are hard to model in arbitrary dielectric environment. Here, we develop a formalism that allows the embedding of emitters to a wide class of thin curved waveguides, by greatly simplifying the wave equation and consequentially the dipole interactions. We demonstrate the formalism for locally constant positive curved surfaces, where we derive a new surface Green function that allows exact computation of the collective superradiant and subradiant states. We also show how the curvature and the thickness of the waveguides affects the collective states through an effective surface wavelength.

We consider the D4-D8-D8 brane system which serves as ultraviolet completion of the Nambu-Jona-Lasinio model, where the only degrees of freedom carrying baryon charge are fermions. By turning on chemical potential for this charge one may expect the formation of the Fermi liquid ground state. At strong coupling we use the dual holographic description to investigate the responses of the system to small perturbations. In the chirally symmetric phase we find that the density dependent part of the heat capacity vanishes linearly with temperature. We also observe a zero sound excitation in the collisionless regime, whose speed is equal to that of normal sound in the hydrodynamic regime. Both the linear dependence of the heat capacity and the existence of zero sound are properties of the Fermi liquid ground state. We also compute the two-point function of the currents at vanishing frequency but do not find any singularities at finite values of the momentum.

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

Probe branes with finite worldvolume electric flux in the background created by a stack of Dp branes describe holographically strongly interacting fundamental matter at finite density. We identify two quantities whose leading low temperature behavior is independent of the dimensionality of the probe branes: specific heat and DC conductivity. This behavior can be inferred from the dynamics of the fundamental strings which provide a good description of the probe branes in the regime of low temperatures and finite densities. We also comment on the speed of sound on the branes and the temperature dependence of DC conductivity at vanishing charge density.

Autferroics, recently proposed as a sister branch of multiferroics, exhibit strong intrinsic magnetoelectricity, but ferroelectricity and magnetism are mutually exclusive rather than coexisting. Here, a general model is considered based on the Landau theory, to clarify the distinction between multi and autferroics by qualitative change-rotation in Landau free energy landscape and in particular phase mapping. The TiGeSe_3 exemplifies a factual material, whose first-principles computed Landau coefficients predict its autferroicity. Our investigations pave the way for an alternative avenue in the pursuit of intrinsically strong magnetoelectrics.

Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase unceasingly. This growth of the deep learning models is accompanied by issues related to their considerable energy consumption, both during the training and inference phases, as well as their scalability. Although a number of work based on unconventional physical systems have been proposed which addresses the issue of energy efficiency in the inference phase, efficient training of deep learning models has remained unaddressed. So far, training of digital deep learning models mainly relies on backpropagation, which is not suitable for physical implementation as it requires perfect knowledge of the computation performed in the so-called forward pass of the neural network. Here, we tackle this issue by proposing a simple deep neural network architecture augmented by a biologically plausible learning algorithm, referred to as "model-free forward-forward training". The proposed architecture enables training deep physical neural networks consisting of layers of physical nonlinear systems, without requiring detailed knowledge of the nonlinear physical layers' properties. We show that our method outperforms state-of-the-art hardware-aware training methods by improving training speed, decreasing digital computations, and reducing power consumption in physical systems. We demonstrate the adaptability of the proposed method, even in systems exposed to dynamic or unpredictable external perturbations. To showcase the universality of our approach, we train diverse wave-based physical neural networks that vary in the underlying wave phenomenon and the type of non-linearity they use, to perform vowel and image classification tasks experimentally.

Clifford-Steerable CNNs (CSCNNs) provide a unified framework that allows incorporating equivariance to arbitrary pseudo-Euclidean groups, including isometries of Euclidean space and Minkowski spacetime. In this work, we demonstrate that the kernel basis of CSCNNs is not complete, thus limiting the model expressivity. To address this issue, we propose Conditional Clifford-Steerable Kernels, which augment the kernels with equivariant representations computed from the input feature field. We derive the equivariance constraint for these input-dependent kernels and show how it can be solved efficiently via implicit parameterization. We empirically demonstrate an improved expressivity of the resulting framework on multiple PDE forecasting tasks, including fluid dynamics and relativistic electrodynamics, where our method consistently outperforms baseline methods.

The rapid data surge from the high-luminosity Large Hadron Collider introduces critical computational challenges requiring novel approaches for efficient data processing in particle physics. Quantum machine learning, with its capability to leverage the extensive Hilbert space of quantum hardware, offers a promising solution. However, current quantum graph neural networks (GNNs) lack robustness to noise and are often constrained by fixed symmetry groups, limiting adaptability in complex particle interaction modeling. This paper demonstrates that replacing the Lorentz Group Equivariant Block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using nearly 5.5 times fewer parameters. Additionally, quantum circuits effectively replace MLPs by inherently preserving symmetries, with Lorentz symmetry integration ensuring robust handling of relativistic invariance. Our Lorentz-Equivariant Quantum Graph Neural Network (Lorentz-EQGNN) achieved 74.00% test accuracy and an AUC of 87.38% on the Quark-Gluon jet tagging dataset, outperforming the classical and quantum GNNs with a reduced architecture using only 4 qubits. On the Electron-Photon dataset, Lorentz-EQGNN reached 67.00% test accuracy and an AUC of 68.20%, demonstrating competitive results with just 800 training samples. Evaluation of our model on generic MNIST and FashionMNIST datasets confirmed Lorentz-EQGNN's efficiency, achieving 88.10% and 74.80% test accuracy, respectively. Ablation studies validated the impact of quantum components on performance, with notable improvements in background rejection rates over classical counterparts. These results highlight Lorentz-EQGNN's potential for immediate applications in noise-resilient jet tagging, event classification, and broader data-scarce HEP tasks.

A refined semi-holographic non-Fermi liquid model, in which carrier electrons hybridize with operators of a holographic critical sector, has been proposed recently for strange metallic behavior. The model, consistently with effective theory approach, has two couplings whose ratio is related to the doping. We explain the origin of the linear-in-T resistivity and strange metallic behavior as a consequence of the emergence of a universal form of the spectral function which is independent of the model parameters when the ratio of the two couplings take optimal values determined only by the critical exponent. This universal form fits well with photoemission data of copper oxide samples for under/optimal/over-doping with a fixed exponent over a wide range of temperatures. We further obtain a refined Planckian dissipation scenario in which the scattering time τ= f cdot hbar /(k_B T), with f being O(1) at strong coupling, but O(10) at weak coupling.

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields an implicit solvent method identical in form to the Molecular Density Functional theory of Borgis et. al., but with an explicit formula for the 'ideal' free energy term. This new expression for the ideal free energy term can be computed from all-atom molecular dynamics of a solvent with only short-range interactions. The key hypothesis required to make the theory valid is that all smooth (and hence long-range) energy functions obey Gaussian statistics. This is essentially a random phase approximation for perturbations from a short-range only, 'reference,' fluid. This single hypothesis is enough to prove that the self-consistent LMF procedure minimizes a novel density functional whose 'ideal' free energy is the molecular system under a specific, reference Hamiltonian, as opposed to the non-interacting gas of conventional density functionals. Implementation of this new functional into existing software should be straightforward and robust.

In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether's theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of "implicit adaptive optimization", establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

In this paper, we aim to examine the electric Penrose process (PP) around a charged black hole in 4D Einstein-Gauss-Bonnet (EGB) gravity and bring out the effect of the Gauss-Bonnet (GB) coupling parameter alpha and black hole charge on the efficiency of the energy extraction from the black hole. This research is motivated by the fact that electrostatic interactions significantly influence the behavior of charged particles in the vicinity of a charged static black hole. Under this interaction, decaying charged particles can have negative energies, causing energy to be released from black holes with no ergosphere. We show that the GB coupling parameter has a significant impact on the energy efficiency of the electric PP, but the efficiency can be strongly enhanced by the black hole charge due to the Coulomb force. Finally, we consider the accretion disk around the black hole and investigate in detail its radiation properties, such as the electromagnetic radiation flux, the temperature, and the differential luminosity. We show that the GB coupling parameter can have a significant impact on the radiation parameters, causing them to increase in the accretion disk in the vicinity of the black hole. Interestingly, it is found that the 4D EGB charged black hole is more efficient and favorable for the accretion disk radiation compared to a charged black hole in Einstein gravity.

It has been suggested previously that an ultra-soft fermionic excitation develops, albeit with a small spectral weight, in a system of massless fermions and scalar bosons with Yukawa interaction at high temperature (T). In this paper we study how this excitation is modified at finite chemical potential (μ). We relate the existence of the ultra-soft mode to symmetries, in particular charge conjugation, and a supersymmetry of the free system which is spontaneously broken by finite temperature and finite density effects, as argued earlier by Lebedev and Smilga. A non vanishing chemical potential breaks both symmetries explicitly, and maximally at zero temperature where the mode ceases to exist. A detailed calculation indicates that the ultra-soft excitation persists as long as Tgtrsim μ.

Aims: The aim of the present study is to explore how to disentangle energy-dependent time delays due to a possible Lorentz invariance violation (LIV) at Planck scale from intrinsic delays expected in standard blazar flares. Methods: We first characterise intrinsic time delays in BL Lacs and Flat Spectrum Radio Quasars in standard one-zone time-dependent synchrotron self-Compton or external Compton models, during flares produced by particle acceleration and cooling processes. We simulate families of flares with both intrinsic and external LIV-induced energy-dependent delays. Discrimination between intrinsic and LIV delays is then investigated in two different ways. A technique based on Euclidean distance calculation between delays obtained in the synchrotron and in the inverse-Compton spectral bumps is used to assess their degree of correlation. A complementary study is performed using spectral hardness versus intensity diagrams in both energy ranges. Results: We show that the presence of non-negligible LIV effects, which essentially act only at very high energies (VHE), can drastically reduce the strong correlation expected between the X-ray and the VHE gamma-ray emission in leptonic scenarios. The LIV phenomenon can then be hinted at measuring the Euclidean distance d_{E} from simultaneous X-ray and gamma-ray flare monitoring. Large values of minimal distance d_{E,min} would directly indicate the influence of non-intrinsic time delays possibly due to LIV in SSC flares. LIV effects can also significantly modify the VHE hysteresis patterns in hardness-intensity diagrams and even change their direction of rotation as compared to the X-ray behaviour. Both observables could be used to discriminate between LIV and intrinsic delays, provided high quality flare observations are available.

Whilst most of the binary configurations in modified theories of gravity are studied under quasi-circular orbit limit, eccentricity effects could play a significant role in future gravitational wave detections. We derive the gravitational radiation-reaction force for nonspinning eccentric orbits within the effective-one-body (EOB) description for the massless scalar-tensor theories up to 1.5 post-Newtonian (PN) order. The effects in such theories start at 1/c^3 and interestingly, the 1.5PN order effect is due to the radiation reaction square effects which is a conservative effect. The results derived here can be implemented in the quasi-circular EOB-based waveform models to construct waveform templates for generic orbit binaries within massless scalar-tensor theories of gravity.

The tradeoff between precision and performance in molecular simulations can nowadays be addressed by machine-learned force fields (MLFF), which combine ab initio accuracy with force field numerical efficiency. Different from conventional force fields however, incorporating relevant electronic degrees of freedom into MLFFs becomes important. Here, we implement an equivariant transformer that embeds molecular net charge and spin state without additional neural network parameters. The model trained on a singlet/triplet non-correlated CH2 dataset can identify different spin states and shows state-of-the-art extrapolation capability. Therein, self-attention sensibly captures non-local effects, which, as we show, can be finely tuned over the network hyper-parameters. We indeed found that Softmax activation functions utilised in the self-attention mechanism of graph networks outperformed ReLU-like functions in prediction accuracy. Increasing the attention temperature from τ= d to 2d further improved the extrapolation capability, indicating a weighty role of nonlocality. Additionally, a weight initialisation method was purposed that sensibly accelerated the training process.

High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation. While Conditional Flow Matching (CFM) offers a robust acceleration approach, we demonstrate its standard training loss is fundamentally misleading. Specifically, utilizing a Jefferson Lab Nuclear Physics (NP) kinematic dataset (γp to ρ^0 p to π^+π^- p), we expose that CFM loss plateaus prematurely, obscuring ongoing physical refinement. To verify this disconnect is a dataset-agnostic pathology, we introduce ScatterPrism, an efficient generative surrogate evaluated against both the NP data and synthetic stress tests modeling challenging 1D distribution topologies. Coupling these benchmarks, we establish that physics-informed metrics continue improving long after standard loss converges. Consequently, we propose a multi-metric diagnostic protocol to ensure true kinematic fidelity without data memorization. Driven by NP challenges relevant to the forthcoming Electron-Ion Collider (EIC), this unified machinery has strong potential to extend to High-Energy Physics (HEP) applications, such as jet modeling. Furthermore, the framework holds promise for broader domains requiring rigorous generative reliability, including medical imaging, astrophysics, and quantitative finance.

Large language models (LLMs) can be adapted to new tasks using parameter-efficient fine-tuning (PEFT) methods that modify only a small number of trainable parameters, often through low-rank updates. In this work, we adopt a quantum-information-inspired perspective to understand their effectiveness. From this perspective, low-rank parameterizations naturally correspond to low-dimensional Matrix Product States (MPS) representations, which enable entanglement-based characterizations of parameter structure. Thereby, we term and measure "Artificial Entanglement", defined as the entanglement entropy of the parameters in artificial neural networks (in particular the LLMs). We first study the representative low-rank adaptation (LoRA) PEFT method, alongside full fine-tuning (FFT), using LLaMA models at the 1B and 8B scales trained on the Tulu3 and OpenThoughts3 datasets, and uncover: (i) Internal artificial entanglement in the updates of query and value projection matrices in LoRA follows a volume law with a central suppression (termed as the "Entanglement Valley"), which is sensitive to hyper-parameters and is distinct from that in FFT; (ii) External artificial entanglement in attention matrices, corresponding to token-token correlations in representation space, follows an area law with logarithmic corrections and remains robust to LoRA hyper-parameters and training steps. Drawing a parallel to the No-Hair Theorem in black hole physics, we propose that although LoRA and FFT induce distinct internal entanglement signatures, such differences do not manifest in the attention outputs, suggesting a "no-hair" property that results in the effectiveness of low rank updates. We further provide theoretical support based on random matrix theory, and extend our analysis to an MPS Adaptation PEFT method, which exhibits qualitatively similar behaviors.

We present a new approach to constructing and fitting dipoles and higher-order multipoles in synthetic galaxy samples over the sky. Within our Bayesian paradigm, we illustrate that this technique is robust to masked skies, allowing us to make credible inferences about the relative contributions of each multipole. We also show that dipoles can be recovered in surveys with small footprints, determining the requisite source counts required for concrete estimation of the dipole parameters. This work is motivated by recent probes of the cosmic dipole in galaxy catalogues. Namely, the kinematic dipole of the Cosmic Microwave Background, as arising from the motion of our heliocentric frame at approx 370 km,s^{-1}, implies that an analogous dipole should be observed in the number counts of galaxies in flux-density-limited samples. Recent studies have reported a dipole aligning with the kinematic dipole but with an anomalously large amplitude. Accordingly, our new technique will be important as forthcoming galaxy surveys are made available and for revisiting previous data.

We analyze Muon as originally proposed and used in practice -- using the momentum orthogonalization with a few Newton-Schulz steps. The prior theoretical results replace this key step in Muon with an exact SVD-based polar factor. We prove that Muon with Newton-Schulz converges to a stationary point at the same rate as the SVD-polar idealization, up to a constant factor for a given number q of Newton-Schulz steps. We further analyze this constant factor and prove that it converges to 1 doubly exponentially in q and improves with the degree of the polynomial used in Newton-Schulz for approximating the orthogonalization direction. We also prove that Muon removes the typical square-root-of-rank loss compared to its vector-based counterpart, SGD with momentum. Our results explain why Muon with a few low-degree Newton-Schulz steps matches exact-polar (SVD) behavior at a much faster wall-clock time and explain how much momentum matrix orthogonalization via Newton-Schulz benefits over the vector-based optimizer. Overall, our theory justifies the practical Newton-Schulz design of Muon, narrowing its practice-theory gap.

Initial states of dense matter with nonzero electron chiral imbalance could potentially give rise to strong magnetic fields through chiral plasma instability. Previous work indicated that unless chiral chemical potential is as large as the electron vector chemical potential, the growth of magnetic fields due to the instability is washed out by chirality flipping rate enabled by electron mass. We re-examine this claim in a broader range of parameters and find that at higher temperatures the hierarchy is reversed supporting a growing magnetic field for an initial electron chiral chemical potential much smaller than the electron vector chemical potential. Further, we identify a qualitatively new effect relevant for magnetized hot and dense medium where chiral magnetic effect (CME) sourced by density fluctuation acts as a powerful source of Joule heating. Remarkably, even modest chiral chemical potentials (keV) in such environment can deposit energy densities set by the QCD scale in a relatively short time of the order of a few milliseconds or seconds. We speculate how this mechanism makes CME-driven Joule heating a potentially critical ingredient in the dynamics of turbulent density fluctuation of supernovae and neutron star mergers.

Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, applying different PINNs to solve the equation in each subdomain and aligning the solution at the interface of the subdomains. Hence, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of the multi-domain PINNs is sensitive to the choice of the interface conditions for solution alignment. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine the optimal interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit models. The first one applies to the entire training procedure, and online updates a Gaussian process (GP) reward surrogate that given the PDE parameters and interface conditions predicts the solution error. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP surrogate for each phase to enable different condition selections at the two stages so as to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.

We describe in the context of the particle physics (PP) standard model (SM) `PP-SM' the understanding of the primordial properties and composition of the Universe in the temperature range 130GeV>T>20keV. The Universe evolution is described using FLRW cosmology. We present a global view on particle content across time and describe the different evolution eras using deceleration parameter q. We follow the arrow of time in the expanding and cooling Universe: After the PP-SM heavies (t, h, W, Z) diminish in abundance below Tsimeq 50GeV, the PP-SM plasma in the Universe is governed by the strongly interacting Quark-Gluon content. Once the temperature drops below Tsimeq 150MeV, quarks and gluons hadronize into strongly interacting matter particles. Rapid disappearance of baryonic antimatter completes at T_B=38.2MeV. We study the ensuing disappearance of strangeness and mesons in general. We show that the different eras defined by particle populations are barely separated from each other with abundance of muons fading out just prior to T=O(2.5)MeV, the era of emergence of the free-streaming neutrinos. We discuss the two relevant fundamental constants controlling the decoupling of neutrinos. We subsequently follow the primordial Universe as it passes through the hot dense electron-positron plasma epoch. The high density of positron antimatter disappears near T=20.3keV: Nuclear reactions occur in the presence of a highly mobile and relatively strongly interacting electron-positron plasma phase. We apply plasma theory methods to describe the strong screening effects between heavy dust particle (nucleons). We analyze the paramagnetic characteristics of the electron-positron plasma when exposed to an external primordial magnetic field.

We introduce Orb-v3, the next generation of the Orb family of universal interatomic potentials. Models in this family expand the performance-speed-memory Pareto frontier, offering near SoTA performance across a range of evaluations with a >10x reduction in latency and > 8x reduction in memory. Our experiments systematically traverse this frontier, charting the trade-off induced by roto-equivariance, conservatism and graph sparsity. Contrary to recent literature, we find that non-equivariant, non-conservative architectures can accurately model physical properties, including those which require higher-order derivatives of the potential energy surface. This model release is guided by the principle that the most valuable foundation models for atomic simulation will excel on all fronts: accuracy, latency and system size scalability. The reward for doing so is a new era of computational chemistry driven by high-throughput and mesoscale all-atom simulations.

Context. Low-mass bodies, such as comets, asteroids, planetesimals, and free-floating planets, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems. These can be modeled as massless particles (MLPs, hereafter). The dynamics of large populations of MLPs, however, has yet received little attention in literature. Aims. We investigate the dynamical evolution of MLP populations in star clusters, and characterize their kinematics and ejection rates. Methods. We present NBODY6++GPU-MASSLESS, a modified version of the N-body simulation code NBODY6++GPU, that allows fast integration of star clusters that contain large numbers of massless particles (MLPs). NBODY6++GPU-MASSLESS contains routines specifically directed at the dynamical evolution of low-mass bodies, such as planets. Results. Unlike stars, MLPs do not participate in the mass segregation process. Instead, MLPs mostly follow the gravitational potential of the star cluster, which gradually decreases over time due to stellar ejections and stellar evolution. The dynamical evolution of MLPs is primarily affected by the evolution of the core of the star cluster. This is most apparent in the outer regions for clusters with higher initial densities. High escape rates of MLPs are observed before the core-collapse, after which escape rates remain stable. Denser star clusters undergo a more intense core collapse, but this does not impact the dynamical evolution of MLPs. The speeds of escaping stars are similar to those of escaping MLPs, when disregarding the high-velocity ejections of neutron stars during the first 50 Myr.

Foundation Models are neural networks that are capable of simultaneously solving many problems. Large Language Foundation Models like ChatGPT have revolutionized many aspects of daily life, but their impact for science is not yet clear. In this paper, we use a new Foundation Model for hadronic jets to solve three key challenges in collider physics. In particular, we show how experiments can (1) save significant computing power when developing reconstruction algorithms, (2) perform a complete uncertainty quantification for high-dimensional measurements, and (3) search for new physics with model agnostic methods using low-level inputs. In each case, there are significant computational or methodological challenges with current methods that limit the science potential of deep learning algorithms. By solving each problem, we take jet Foundation Models beyond proof-of-principle studies and into the toolkit of practitioners.

The Sun's outer atmosphere, the corona, is maintained at mega-Kelvin temperatures and fills the heliosphere with a supersonic outflowing wind. The dissipation of magnetic waves and direct electric currents are likely to be the most significant processes for heating the corona, but a lively debate exists on their relative roles. Here, we suggest that the two are often intrinsically linked, since magnetic waves may trigger current dissipation, and impulsive reconnection can launch magnetic waves. We present a study of the first of these processes by using a 2D physics-based numerical simulation using the Adaptive Mesh Refined (AMR) Versatile Advection Code (VAC). Magnetic waves such as fast magnetoacoustic waves are often observed to propagate in the large-scale corona and interact with local magnetic structures. The present numerical simulations show how the propagation of magnetic disturbances towards a null point or separator can lead to the accumulation of the electric currents. Lorentz forces can laterally push and vertically stretch the magnetic fields, forming a current sheet with a strong magnetic-field gradient. The magnetic field lines then break and reconnect, and so contribute towards coronal heating. Numerical results are presented that support these ideas and support the concept of a symbiosis between waves and reconnection in heating the solar corona.

We present the wakefield conformal mapping technique that can be readily applied to the analysis of the radiation generated by an ultra-relativistic particle in the step transition and a collimator. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections, as well as become a useful tool in the shape optimization problems.

Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary losses. We show that this supervision term acts as an operator-level preconditioner: for suitable weights, our comparison bounds guarantee a substantially smaller condition number than under the standard PINN loss, independently of how the pointwise labels are obtained. For a broad class of PDEs admitting a Feynman-Kac (FK) representation, we generate such labels by Monte Carlo averages of the FK functional, resulting in what we call ``FK-PINNs", and using the excess risk decomposition approach, we derive non-asymptotic L^2(Ω)-error bounds for FK-PINNs with tanh activation trained by finitely many steps of gradient descent. Along the way, we establish pseudo-dimension bounds for first- and second-order derivatives of tanh neural networks, which are of independent interest and, to the best of our knowledge, new. Numerical experiments on Poisson, Schrödinger, mean exit time, and committor problems corroborate the theory, and show that FK-PINNs can successfully solve PDEs for which standard PINNs exhibit severe failure modes.

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/GradientPathologiesPINNs.

High Power Laser's (HPL) optimal performance is essential for the success of a wide variety of experimental tasks related to light-matter interactions. Traditionally, HPL parameters are optimised in an automated fashion relying on black-box numerical methods. However, these can be demanding in terms of computational resources and usually disregard transient and complex dynamics. Model-free Deep Reinforcement Learning (DRL) offers a promising alternative framework for optimising HPL performance since it allows to tune the control parameters as a function of system states subject to nonlinear temporal dynamics without requiring an explicit dynamics model of those. Furthermore, DRL aims to find an optimal control policy rather than a static parameter configuration, particularly suitable for dynamic processes involving sequential decision-making. This is particularly relevant as laser systems are typically characterised by dynamic rather than static traits. Hence the need for a strategy to choose the control applied based on the current context instead of one single optimal control configuration. This paper investigates the potential of DRL in improving the efficiency and safety of HPL control systems. We apply this technique to optimise the temporal profile of laser pulses in the L1 pump laser hosted at the ELI Beamlines facility. We show how to adapt DRL to the setting of spectral phase control by solely tuning dispersion coefficients of the spectral phase and reaching pulses similar to transform limited with full-width at half-maximum (FWHM) of ca1.6 ps.

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

We study an autonomous model of a Maxwell demon that works by rectifying thermal fluctuations of chemical reactions. It constitutes the chemical analog of a recently studied electronic demon. We characterize its scaling behavior in the macroscopic limit, its performances, and the impact of potential internal delays. We obtain analytical expressions for all quantities of interest, namely, the generated reverse chemical current, the output power, the transduction efficiency, and the correlations between the numbers of molecules. Due to a bound on the nonequilibrium response of its chemical reaction network, we find that, contrary to the electronic case, there is no way for the Maxwell demon to generate a finite output in the macroscopic limit. Finally, we analyze the information thermodynamics of the Maxwell demon from a bipartite perspective. In the limit of a fast demon, the information flow is obtained, its pattern in the state space is discussed, and the behavior of the partial efficiencies related to the measurement and the feedback processes is examined.

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS_{5}) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into scalar-type and vector-type components according to their tensorial behavior on the three-sphere. Two degrees of freedom of the field are described by scalar-type components, which are coupled due to the mass term, while the remaining two degrees of freedom are described by a vector-type component, which decouples completely. Motivated by the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz in the limit of zero spin, we use a field transformation to decouple the scalar-type components at the expense of introducing a complex separation parameter β. This parameter can be determined analytically, and its values correspond to two distinct polarizations of the scalar-type sector: "electromagnetic" and "non-electromagnetic", denoted by β_{+} and β_{-}, respectively. In the scalar-type sector, the radial differential equation for each polarization is a Fuchsian differential equation with five singularities, whereas in the vector-type sector, the radial equation has four singularities. By means of the isomonodromy method, we reformulate the boundary value problem in terms of the initial conditions of the Painlevé VI τ function and, using a series expansion of the τ function, we compute the scalar-type and vector-type quasinormal modes (QNMs) in the small horizon limit. Our results are in overall very good agreement with those obtained via the numerical integration method. This shows that the isomonodromy method is a reliable method to compute quasinormal modes in the small horizon limit with high accuracy.

This review presents recent breakthroughs in the realm of nonlinear Hall effects, emphasizing central theoretical foundations and recent experimental progress. We elucidate the quantum origin of the second-order Hall response, focusing on the Berry curvature dipole, which may arise in inversion symmetry broken systems. The theoretical framework also reveals the impact of disorder scattering effects on the nonlinear response. We further discuss the possibility of obtaining nonlinear Hall responses beyond the second order. We examine symmetry-based indicators essential for the manifestation of nonlinear Hall effects in time-reversal symmetric crystals, setting the stage for a detailed exploration of theoretical models and candidate materials predicted to exhibit sizable and tunable Berry curvature dipole. We summarize groundbreaking experimental reports on measuring both intrinsic and extrinsic nonlinear Hall effects across diverse material classes. Finally, we highlight some of the other intriguing nonlinear effects, including nonlinear planar Hall, nonlinear anomalous Hall, and nonlinear spin and valley Hall effects. We conclude with an outlook on pivotal open questions and challenges, marking the trajectory of this rapidly evolving field.

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g phi^3 QFT, by using the retarded/advanced (R/A) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping d<4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Sigma_{F}(p_0) does not vanish when |p_0|rightarrowinfty and cannot be split to retarded and advanced parts. In the Glaser--Epstein approach, the causality is repaired in the composite object G_F(p_0)Sigma_{F}(p_0). In the FTP approach, after repairing the vertices, the corresponding composite objects are G_R(p_0)Sigma_{R}(p_0) and Sigma_{A}(p_0)G_A(p_0). In the limit drightarrow 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition langle 0|phi|0rangle =0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit trightarrow infty .

We investigate magnetic-field amplification driven by the nonresonant hybrid (NRH or Bell) instability and its impact on cosmic-ray (CR) acceleration at reverse shocks of ultrafast outflows (UFOs) from active galactic nuclei (AGN). Previous kinetic studies by particle-in-cell simulations have demonstrated that when maximum CR energy is near the injection scale, NRH instability efficiently amplifies magnetic field up to the saturation level. However, the efficiency of NRH instability goes down as maximum energy increase since CR current is carried by escaping CRs near the maximum energy. We employ a one-dimensional MHD--CR framework solving telegraph-type diffusion--convection equations to trace the coupled evolution of CRs, magnetic fields, and shock dynamics under realistic parameters. We find a distinct transition with magnetic field strength: for weak background fields (B_{0}!lesssim!10^{-4},G), NRH instability efficiently amplifies upstream turbulence, driving a self-regulated state where E_{max} becomes independent of initial strength of magnetic turbulence. In contrast, for stronger background fields (B_{0}!gtrsim!10^{-3},G), the escaping CR current is too weak to drive NRH instability, and magnetic turbulence further decays through parametric instabilities, potentially reducing the acceleration efficiency. We give the physical interpretation for the transition and discuss conditions for PeV--EeV acceleration at UFO reverse shocks.

Single-minus tree-level n-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into n-1 plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.

Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, e.g., uncertainty quantification, remeshing applications, topology optimization, and so forth. This limitation has motivated the application of data-driven surrogate models, where the microscale computations are substituted with a surrogate, usually acting as a black-box mapping between macroscale quantities. These models offer significant speedups but struggle with incorporating microscale physical constraints, such as the balance of linear momentum and constitutive models. In this contribution, we propose Equilibrium Neural Operator (EquiNO) as a complementary physics-informed PDE surrogate for predicting microscale physics and compare it with variational physics-informed neural and operator networks. Our framework, applicable to the so-called multiscale FE^{,2}, computations, introduces the FE-OL approach by integrating the finite element (FE) method with operator learning (OL). We apply the proposed FE-OL approach to quasi-static problems of solid mechanics. The results demonstrate that FE-OL can yield accurate solutions even when confronted with a restricted dataset during model development. Our results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers an optimal balance between data-driven and physics-based strategies.

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -- Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equation. Only in this case the electric impedance of a cell can be determined as the ratio between the applied difference of potential and the current across the cell. We show that in the case of anomalous diffusion, the model predicts for the electric impedance of the cell a constant phase element behaviour in the low frequency region. In the parametric curve of the reactance versus the resistance, the slope coincides with the order of the fractional time derivative.

At high-energy collider experiments, generative models can be used for a wide range of tasks, including fast detector simulations, unfolding, searches of physics beyond the Standard Model, and inference tasks. In particular, it has been demonstrated that score-based diffusion models can generate high-fidelity and accurate samples of jets or collider events. This work expands on previous generative models in three distinct ways. First, our model is trained to generate entire collider events, including all particle species with complete kinematic information. We quantify how well the model learns event-wide constraints such as the conservation of momentum and discrete quantum numbers. We focus on the events at the future Electron-Ion Collider, but we expect that our results can be extended to proton-proton and heavy-ion collisions. Second, previous generative models often relied on image-based techniques. The sparsity of the data can negatively affect the fidelity and sampling time of the model. We address these issues using point clouds and a novel architecture combining edge creation with transformer modules called Point Edge Transformers. Third, we adapt the foundation model OmniLearn, to generate full collider events. This approach may indicate a transition toward adapting and fine-tuning foundation models for downstream tasks instead of training new models from scratch.

Large Language Models (LLMs) have achieved remarkable progress on advanced reasoning tasks such as mathematics and coding competitions. Meanwhile, physics, despite being both reasoning-intensive and essential to real-world understanding, received limited academic and industrial attention. This paper introduces PHYSICS, a dataset containing 16,568 high-quality physics problems spanning subjects and difficulty levels, to facilitate this issue. Specifically, PHYSICS is curated with exercises from over 100 textbooks through a carefully designed pipeline for quality control. It covers five major physics domains: Mechanics, Electromagnetism, Thermodynamics, Optics, and Modern Physics. It also spans a wide range of difficulty levels, from high school to graduate-level physics courses. To utilize the data for improving and evaluating the model's physical reasoning capabilities, we split the dataset into training and test sets, and provide reasoning paths generated by powerful reasoning models for the training data to facilitate model training. In addition, for the evaluation part, we find that existing evaluation frameworks exhibit biases in aspects such as units, simplification, and precision in physics domain. To balance efficiency and accuracy, we introduce a Rule+Model evaluation framework tailored to physics problems. Our evaluations on current state-of-the-art open-source and proprietary models highlight the limitations of current models in handling physics-related tasks. We hope that our dataset and evaluation methodology will jointly advance the development of LLMs in the field of physics.

We present the 2D gyrofluid magnetic reconnection code GREENY (Gyrofluid Reconnection with Extended Electromagnetic Nonlinearity). After a brief introduction to gyrofluids, magnetic reconnection, and the implemented models, we discuss the numerical framework and the algorithmic treatment of the quasi-neutrality condition and Amperè's law. Next, we present solver tests, conservation laws, and the influence of artificial subgrid dissipation on Harris-sheet magnetic reconnection. Finally, we show different applications, initial conditions and present example simulations.

Learning-based simulation of multi-object rigid-body dynamics remains difficult because contact is discontinuous and errors compound over long horizons. Most existing methods remain tied to mesh connectivity and vertex-level message passing, which limits their applicability to mesh-free inputs such as point clouds and leads to high computational cost. Efficiently modeling high-fidelity rigid-body dynamics from mesh-free representations, therefore, remains challenging. We introduce RigidFormer, an object-centric Transformer-based model that learns mesh-free rigid-body dynamics with controllable integration step sizes. RigidFormer reasons at the object level and advances each object through compact anchors; Anchor-Vertex Pooling enriches these anchors with local vertex features, retaining contact-relevant geometry without dense vertex-level interaction. We propose Anchor-based RoPE to inject anchor geometry into attention while respecting the unordered nature of objects and anchors: object-token processing is permutation-equivariant, and the mean-pooled anchor descriptor is invariant to anchor reindexing while preserving shape extent. RigidFormer further enforces rigidity by projecting updates onto the rigid-body manifold using differentiable Kabsch alignment. On standard benchmarks, RigidFormer outperforms or matches mesh-based baselines using point inputs, runs faster, generalizes to unseen point resolutions and across datasets, and scales to 200+ objects; we also show a preliminary extension to command-conditioned articulated bodies by treating body parts as interacting object-level components.

With the success of static black-hole imaging, the next frontier is the dynamic and 3D imaging of black holes. Recovering the dynamic 3D gas near a black hole would reveal previously-unseen parts of the universe and inform new physics models. However, only sparse radio measurements from a single viewpoint are possible, making the dynamic 3D reconstruction problem significantly ill-posed. Previously, BH-NeRF addressed the ill-posed problem by assuming Keplerian dynamics of the gas, but this assumption breaks down near the black hole, where the strong gravitational pull of the black hole and increased electromagnetic activity complicate fluid dynamics. To overcome the restrictive assumptions of BH-NeRF, we propose PI-DEF, a physics-informed approach that uses differentiable neural rendering to fit a 4D (time + 3D) emissivity field given EHT measurements. Our approach jointly reconstructs the 3D velocity field with the 4D emissivity field and enforces the velocity as a soft constraint on the dynamics of the emissivity. In experiments on simulated data, we find significantly improved reconstruction accuracy over both BH-NeRF and a physics-agnostic approach. We demonstrate how our method may be used to estimate other physics parameters of the black hole, such as its spin.