Daily Papers

In the mid-twentieth century, mathematician and polymath John von Neumann created a computational system on an array of cells as a simple model of the human brain, where each cell had one of a finite set of roles or states that he predicted would be modelled by a diffusion process. In this work, we show that such a system, when developed in a modern deep learning setting, enables the construction of an artificial neuron having specialized roles that can be learnt. We refer to this neuron as the Von Neumann neuron, and the resulting neural network from such neurons result in a self-engineered design whose architecture is only dependent on the structure and locations of its inputs and outputs on this cellular array. The mathematical framework for these Von Neumann Networks (VNNs) is also constructed and shows that they are based on the extension of neural operators and the learning of Green's functions with convolutions on a cellular topology having a diffusion signature. We also prove that these VNNs are part of a more general computational system called Cellular Machines that are computationally universal. Initial experiments show that VNN based multi-layered perceptrons outperform their equivalent deep learning variant on basic tasks, while being more parameter efficient and are capable of learning new types of tasks. This includes the ability to solve for and construct an extension of the Von Neumann (hardware) architecture common to all modern computers to cells and suggests new opportunities that could be explored.

In this paper, we prove the existence of stationary pulse solutions for a bulk-surface reaction-diffusion system modeling cell polarization in two-dimensional domains. Using a singular perturbation method, we construct pulse solutions whose centers lie near non-degenerate critical points of a geometry-dependent potential expressed in terms of the Neumann Green's function, as formally predicted in watanabe2026. The main analytical difficulty arises from the half-Laplacian induced by the logarithmic singularity of the Green's function, resulting in algebraically rather than exponentially decaying inner solutions. Our analysis may also serve as a useful guide for applying singular perturbation methods to other bulk-surface type systems.

We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process. To that end, the asymptotics of Green's functions are determined along all directions. We also find the exit probabilities at the edges, the probability of remaining in the cone forever and the laws of the exit point and exit time. From this, we derive an explicit formula for the transition kernel of the process. These results arise from two different methods initially introduced to study random walks. An analytical approach, developed in the 1970s by Malyshev and based on the steepest descent method on a Riemann surface, is used to determine the asymptotics of the Green's functions. A recursive compensation approach, inspired by the method developed in the 1990s by Adan, Wessels and Zijm, is used to determine the harmonic functions.

A domain wall (DW) which moves parallel to a magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional (2D) metal can pump spin polarization into the metal. It is assumed that localized spins of a collinear AFMI interact with itinerant electrons through their exchange interaction on the interface. We employed the formalism of Keldysh Green's functions for electrons which experience potential and spin-orbit scattering on random impurities. This formalism allows a unified analysis of spin pumping, spin diffusion and spin relaxation effects on a 2D electron gas. It is shown that the pumping of a nonstaggered magnetization into the metal film takes place in the second order with respect to the interface exchange interaction. At sufficiently weak spin relaxation this pumping effect can be much stronger than the first-order effect of the Pauli magnetism which is produced by the small nonstaggered exchange field of the DW. It is shown that the pumped polarization is sensitive to the geometry of the electron's Fermi surface and increases when the wave vector of the staggered magnetization approaches the nesting vector of the Fermi surface. In a disordered diffusive electron gas the induced spin polarization follows the motion of the domain wall. It is distributed asymmetrically around the DW over a distance which can be much larger than the DW width.

There is extensive current interest about electronic topology in correlated settings. In strongly correlated systems, contours of Green's function zeros may develop in frequency-momentum space, and their role in correlated topology has increasingly been recognized. However, whether and how the zeros contribute to electronic properties is a matter of uncertainty. Here we address the issue in an exactly solvable model for Mott insulator. We show that the Green's function zeros contribute to several physically measurable correlation functions, in a way that does not run into inconsistencies. In particular, the physical properties remain robust to chemical potential variations up to the Mott gap as it should be based on general considerations. Our work sets the stage for further understandings on the rich interplay among topology, symmetry and strong correlations.

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96\%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.

Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Due to the complexity in many-electron wavefunctions, machine learning models capable of capturing fundamental many-body physics remain limited. Here, we present a deep learning framework targeting the many-body Green's function, which unifies predictions of electronic properties in ground and excited states, while offering physical insights into many-electron correlation effects. By learning the GW or coupled-cluster self-energy from mean-field features, our graph neural network achieves competitive performance in predicting one- and two-particle excitations and quantities derivable from one-particle density matrix. We demonstrate its high data efficiency and good transferability across chemical species, system sizes, molecular conformations, and correlation strengths in bond breaking, through multiple molecular and nanomaterial benchmarks. This work opens up opportunities for utilizing machine learning to solve many-electron problems.

Electron-electron (e-e) and electron-phonon (e-ph) interactions are challenging to describe in correlated materials, where their joint effects govern unconventional transport, phase transitions, and superconductivity. Here we combine first-principles e-ph calculations with dynamical mean field theory (DMFT) as a step toward a unified description of e-e and e-ph interactions in correlated materials. We compute the e-ph self-energy using the DMFT electron Green's function, and combine it with the e-e self-energy from DMFT to obtain a Green's function including both interactions. This approach captures the renormalization of quasiparticle dispersion and spectral weight on equal footing. Using our method, we study the e-ph and e-e contributions to the resistivity and spectral functions in the correlated metal Sr_2RuO_4. In this material, our results show that e-e interactions dominate transport and spectral broadening in the temperature range we study (50-310~K), while e-ph interactions are relatively weak and account for only sim10\% of the experimental resistivity. We also compute effective scattering rates, and find that the e-e interactions result in scattering several times greater than the Planckian value k_BT, whereas e-ph interactions are associated with scattering rates lower than k_BT. Our work demonstrates a first-principles approach to combine electron dynamical correlations from DMFT with e-ph interactions in a consistent way, advancing quantitative studies of correlated materials.

Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is not halved by conjugate symmetry, HNO retains twice as many frequency corners as FNO but one real weight where FNO carries a complex pair, so the two operators are iso-parametric at equal width and differ only in spectral basis. Our central thesis is that the best basis is a property of the operator. Self-adjoint elliptic operators (Poisson, biharmonic) have real, symmetric Green's functions that the real Hartley multiplier diagonalizes exactly, and HNO is favored there. Time-dependent operators carry phase, from oscillation in the wave equation to transport in advection, Burgers, and Navier-Stokes, which a real diagonal multiplier cannot represent, so FNO is favored there, and increasingly so with the operator's phase content, leaving the phaseless heat equation as the borderline case. Training both operators identically and benchmarking across PDE classes, initial-condition families, and boundary conditions, we find an elliptic-versus-time-dependent split that is monotone in operator phase content and matches the Green's-function theory we develop. Rather than a universal winner, our findings give a predictive rule: match the spectral basis to the symmetry of the solution operator.

We present an escape rate theory for current-induced chemical reactions. We use Keldysh nonequilibrium Green's functions to derive a Langevin equation for the reaction coordinate. Due to the out of equilibrium electronic degrees of freedom, the friction, noise, and effective temperature in the Langevin equation depend locally on the reaction coordinate. As an example, we consider the dissociation of diatomic molecules induced by the electronic current from a scanning tunnelling microscope tip. In the resonant tunnelling regime, the molecular dissociation involves two processes which are intricately interconnected: a modification of the potential energy barrier and heating of the molecule. The decrease of the molecular barrier (i.e. the current induced catalytic reduction of the barrier) accompanied by the appearance of the effective, reaction-coordinate-dependent temperature is an alternative mechanism for current-induced chemical reactions, which is distinctly different from the usual paradigm of pumping vibrational degrees of freedom.

The magnetization in a superconductor induced due to the inverse proximity effect is investigated in hybrid bilayers containing a superconductor and a ferromagnetic insulator or a strongly spin-polarized ferromagnetic metal. The study is performed within a quasiclassical Green function framework, wherein Usadel equations are solved with boundary conditions appropriate for strongly spin-polarized ferromagnetic materials. A comparison with recent experimental data is presented. The singlet to triplet conversion of the superconducting correlations as a result of the proximity effect with a ferromagnet is studied.

The finite-temperature magnetic properties of Fe_xPd_{1-x} and Co_xPt_{1-x} alloys have been investigated. It is shown that the temperature-dependent magnetic behaviour of alloys, composed of originally magnetic and non-magnetic elements, cannot be described properly unless the coupling between magnetic moments at magnetic atoms (Fe,Co) mediated through the interactions with induced magnetic moments of non-magnetic atoms (Pd,Pt) is included. A scheme for the calculation of the Curie temperature (T_C) for this type of systems is presented which is based on the extended Heisenberg Hamiltonian with the appropriate exchange parameters J_{ij} obtained from {\em ab-initio} electronic structure calculations. Within the present study the KKR Green's function method has been used to calculate the J_{ij} parameters. A comparison of the obtained Curie temperatures for Fe_xPd_{1-x} and Co_xPt_{1-x} alloys with experimental data shows rather good agreement.

Describing fermionic systems with attractive interactions, such as superconductors and atomic nuclei, beyond the mean-field level remains a central challenge. In this work, we investigate the performance of Bogoliubov fully self-consistent GW (Bog.~scGW) and second-order Green's function (Bog.~scGF2) methods, implemented within a unified imaginary-time and imaginary-frequency framework. Using the attractive Hubbard model as a benchmark against full configuration interaction (FCI), we find that Bog. scGF2 provides a more accurate description than Bog.~scGW. In particular, Bog.~scGW systematically overestimates the correlation energy, with errors increasing rapidly as the attractive interaction strength grows. These results highlight the importance of exchange contributions in strongly correlated fermionic systems, even when exchange effects are included only at low order in perturbation theory.

Strong correlation brings a rich array of emergent phenomena, as well as a daunting challenge to theoretical physics study. In condensed matter physics, the fractional quantum Hall effect is a prominent example of strong correlation, with Landau level mixing being one of the most challenging aspects to address using traditional computational methods. Deep learning real-space neural network wavefunction methods have emerged as promising architectures to describe electron correlations in molecules and materials, but their power has not been fully tested for exotic quantum states. In this work, we employ real-space neural network wavefunction techniques to investigate fractional quantum Hall systems. On both 1/3 and 2/5 filling systems, we achieve energies consistently lower than exact diagonalization results which only consider the lowest Landau level. We also demonstrate that the real-space neural network wavefunction can naturally capture the extent of Landau level mixing up to a very high level, overcoming the limitations of traditional methods. Our work underscores the potential of neural networks for future studies of strongly correlated systems and opens new avenues for exploring the rich physics of the fractional quantum Hall effect.