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Spontaneous transitions between non-equilibrium patterns are characterised by hydrodynamic calculations of ideal straight roll steady state heat convection. The calculations are tested quantitatively against existing experimental data. |
We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characte... |
Feynman's ratchet is a microscopic machine in contact with two heat reservoirs, at temperatures $T_A$ and $T_B$, that was proposed by Richard Feynman to illustrate the second law of thermodynamics. In equilibrium ($T_A=T_B$), thermal fluctuations prevent the ratchet from generating directed motion. |
We present a truncation scheme of the effective average action approach of the nonperturbative renormalization group which allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The truncation is a natural modification of the standard derivative expansion which... |
We show that mean-field rate equations for submonolayer growth can successfully predict island size distributions in the pre-coalescence regime if the full dependence of capture numbers on both the island size and the coverage is taken into account. This is demonstrated by extensive Kinetic Monte Carlo simulations for... |
The connection between work and changes in the Hamiltonian for a system with a time-dependent Hamiltonian has recently been called into question, casting doubt on the usefulness of the Jarzynski equality for calculating free energy changes. In this paper, we discuss the relationship between two possible definitions of... |
The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. |
The search of controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory. |
In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as $a^{\d... |
We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle nucleation. |
We analyze the correlation properties of the Erdos-Renyi random graph (RG) and the Barabasi-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k_max, representing the local property of the system, shows similar scaling behaviors for random ... |
Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white... |
Using renormalization group methods, we study the Heisenberg-Ising XYZ chain in an external magnetic field directed as the z axis, in the case of small coupling J_3 in the z direction. We study the asymptotic behaviour of the spin space-time correlation function in the direction of the magnetic field and the singulari... |
I present a systematic analysis of formation of the universal annihilation catastrophe which develops in an open system, where species $A$ and $B$ diffuse from the bulk of restricted medium and die on its surface (desorb) by the reaction $A + B \to 0$. This phenomenon arises in the diffusion-controlled limit as a resu... |
Coulomb interactions are present in a wide variety of all-atom force fields. Spherical truncations of these interactions permit fast simulations but are problematic due to their incorrect thermodynamics. |
We consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. |
We study by the perturbative Functional Renormalization Group (FRG) the Random Field and Random Anisotropy O(N) models near $d=4$, the lower critical dimension of ferromagnetism. The long-distance physics is controlled by zero-temperature fixed points at which the renormalized effective action is nonanalytic. |
By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationar... |
First passage under restart has recently emerged as a conceptual framework suitable for the description of a wide range of phenomena, but the endless variety of ways in which restart mechanisms and first passage processes mix and match hindered the identification of unifying principles and general truths. Hope that th... |
Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more classical ones using the actual pair potentials. |
Standard approaches to controlling dynamical systems involve biologically implausible steps such as backpropagation of errors or intermediate model-based system representations. Recent advances in machine learning have shown that "imperfect" feedback of errors during training can yield test performance that is... |
We have studied the superfluid density and the specific heat of the XY model on lattices L x L x H with L >> H (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method. In the H-direction we applied staggered boundary conditions so that the order parameter on the top and bottom layers... |
A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order neighborhood as a network in itself, represented by a corresponding... |
Let L(t) be a Levy flights process with a stability index \alpha\in(0,2), and U be an external multi-well potential. A jump-diffusion Z satisfying a stochastic differential equation dZ(t)=-U'(Z(t-))dt+\sigma(t)dL(t) describes an evolution of a Levy particle of an `instant temperature' \sigma(t) in an external ... |
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal invariant diffusion processes deduced by stochastic variational principles (Nelso... |
Low-energy degrees of freedom of a spin-1/2 kagome antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. |
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical self-similarity through a non-stationary branching process. |
We provide convincing empirical evidence that long range interactions strongly enhance the rectification effect which takes place in mass graded systems. Even more importantly the rectification does not decrease with the increase of the system size. |
We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. |
We present a comprehensive quantum many body theory for kq deformed particles, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles exhibit statistical behaviors that interpolate between conventional bosonic and ferm... |
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is measured. |
As a main example for the superstatistics approach, we study a Brownian particle moving in a d-dimensional inhomogeneous environment with macroscopic temperature fluctuations. We discuss the average occupation time of the particle in spatial cells with a given temperature. |
Within a mean field treatment of the interaction between two oppositely charged plates in a salt free solution, the distance at which a transition from an attractive to a repulsive regime appears can be computed analytically. The mean field description however breaks down under strong coulombic couplings, that can be ... |
Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature, although it does not satisfy the eigenstate thermalization hypothesis. |
A recent model for monodisperse granular suspensions is used to analyze transport properties in spatially inhomogeneous states close to the simple (or uniform) shear flow. The kinetic equation is based on the inelastic Boltzmann (for low density gases) with the presence of a viscous drag force that models the influenc... |
We report laser cooling of fermionic K-40 atoms, with temperatures down to (15 +/- 5) microK, for an enriched sample trapped in a MOT and additionaly cooled in optical molasses. This temperature is a factor of 10 below the Doppler-cooling limit and corresponds to an rms velocity within a factor of two of the lowest re... |
Recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy. Here we further develop this program in the context of a mean-field model, by anal... |
The hypothesis of ``molecular chaos'' is shown to fail when applied to spatially inhomogeneous evolution of a low-density gas, because this hypothesis is incompatible with reduction of interactions of gas particles to ``collisions''. The failure of molecular chaos means existence of statistical correla... |
We have performed multicanonical simulations of hydrophobic-hydrophilic heteropolymers with two simple effective, coarse-grained off-lattice models to study the influence of specific interactions in the models on conformational transitions of selected sequences with 20 monomers. Another aspect of the investigation was... |
Exact propagator of density matrix of particle (electron) under influence of thermal vibrations of its medium (phonons) is treated in simplest approximation beyond the Fermi's golden rule. It is shown that uncertainties \,$\sim\h/t$\, in energy exchanges with the medium give rise to flicker fluctuations in rate of... |
We analyze the influence of classical Gaussian noise on Landau-Zener transitions during a two-level crossing in a time-dependent regular external field. Transition probabilities and coherence factors become random due to the noise. |
We consider an array of XX spin-1/2 chains coupled to acoustic phonons and placed in a magnetic field. Treating the phonons in the mean field approximation, we show that this system presents a first order transition as a function of the magnetic field between a partially magnetized distorted state and the fully polari... |
A simple model of charge transport is provided by a classical particle in a smooth random potential and a dissipative coupling to the environment in the form of Markovian noise and friction. The corresponding Non-Equilibrium Steady State (NESS) can be determined analytically when both the disorder and dissipation are ... |
We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures. It is shown that in the infinite volume limit there arises exactly one vertex of infinite degree and the rest of the tree is distributed like a subcritical Galton-Watson... |
We elucidate the effects of chiral quenched disorder on the scaling properties of pure systems by considering a reduced model that is a variant of the quenched disordered cubic anisotropic O(N) model near its second order phase transition. A generic short-ranged Gaussian disorder distribution is considered. |
We provide the exact generating function for semi-flexible and super-flexible interacting partially directed walks and also analyse the solution in detail. We demonstrate that while fully flexible walks have a collapse transition that is second order and obeys tricritical scaling, once positive stiffness is introduced... |
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. |
To take initial correlations into account, a method, based on the time-independent projection operator technique, that allows converting the conventional linear inhomogeneous (containing a source caused by initial correlations) time-convolution generalized master equation (TC-GME) and time-convolutionless GME (TCL-GME)... |
Within the framework of the instanton approach we present analytical results for the following model problems: (i) particle penetration through a parabolic potential barrier, where the instanton solution practically coincides with the exact (quantum) one; |
We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that ... |
The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of i... |
We determine thresholds $p_c$ for random site percolation on a triangular lattice for neighbourhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN) and next-next-next-next-nearest (5NN) neighbours, and their combinations forming regular hexagons (3NN+2NN+NN, 5NN+4NN+N... |
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters undergo a percolation transition exactly at the critical point. |
The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. |
Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems and to produce a correct density inversion at densities somewhat below the max... |
The positivity of the probability measure of attractively interacting systems of $2N$-component fermions enables the derivation of an exact convexity property for the ground-state energy of such systems. Using analogous arguments, applied to path-integral expressions for the $n$-th Rényi entanglement entropy $S^{}_n$ ... |
We provide a full and unbiased solution to the Dyson-Schwinger equation illustrated for $\phi^4$ theory in 2D. It is based on an exact treatment of the functional derivative $\partial \Gamma / \partial G$ of the 4-point vertex function $\Gamma$ with respect to the 2-point correlation function $G$ within the framework ... |
We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner. The magnetic field ($H$) versus temperature ($T$) phase diagrams for given values of the crystal field $D$ were recovered in accordance to Kaufman and Kanner ... |
Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a ``gravothermal catastrophe'': it can achieve ever increasing values of en... |
We present the solution of a linear Restricted Solid--on--Solid (RSOS) model confined to a slit. We include a field-like energy, which equivalently weights the area under the interface, and also include independent interaction terms with both walls. |
In this paper, we introduce a model for fracture in fibrous materials that takes into account the rupture height of the fibers, in contrast with previous models. Thus, we obtain the profile of the fracture and calculate its roughness, defined as the variance around the mean height. |
The Bose distribution for a gas of nonrelativistic free bosons is derived in the framework of $qp$-deformed second quantization. Some thermodynamical functions for such a system in D dimensions are derived. |
The nonequilibrium critical dynamics of the 2D XY model is investigated numerically through Monte Carlo simulations and analytically in the spin-wave approximation. We focus in particular on the behaviour of the two-time response and correlation functions and show that the ageing dynamics depends on the initial condit... |
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice exhibits an intriguing temperature-driven phase transition in a magnetic field between a classical ferrimagnetic phase and a quantum monomer-dimer phase. A generalized decoration-iteration transformation accurately maps the considered model to a... |
We propose a theory based on simple physical arguments that describes a non equilibrium steady-state by a temperature-like parameter (an "effective temperature"). We show how one can predict the effective temperature as a function of the temperature of the environment for a specific case of non-equilibrium beh... |
We address the effect of disorder geometry on the critical force in disordered elastic systems. We focus on the model system of a long-range elastic line driven in a random landscape. |
We investigate the ground state properties of a one-dimensional two-component ultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solution is used to calculate the many-body wave function of the system. |
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of... |
In this paper, we study a macroscopic system of electrically interacting metallic beads organized as a sequence along an annulus. A random mechanical shaking mimics the thermal excitation. |
Recently Prosen and Mejía-Monasterio (J. Phys. |
Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly decaying persistent power-law correlations between the waiting times as two generic ex... |
We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal Mode or INM spectra) a... |
The two-time correlation function of the displacement of a free quantum Brownian particle with respect to its position at a given time is calculated analytically in the framework of the Caldeira and Leggett ohmic dissipation model (linear coupling of the particle with a thermal bath with a continuum of modes, proportio... |
Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. |
In the first part of the article, we study one-dimensional noninteracting fermions in the continuum and in the presence of the repulsive inverse power law potential, with an emphasis on the Wigner function in the semiclassical limit. In this limit, the Wigner function exhibits an edge called the Fermi surf that depend... |
The memory and rejuvenation aspects of intermittent heat transport are explored theoretically and by numerical simulation for Ising spin glasses with short-ranged interactions. The theoretical part develops a picture of non-equilibrium glassy dynamics recently introduced by the authors. |
The spin-1 Ising-Heisenberg diamond chain in a magnetic field is exactly solved by a rigorous treatment based on the transfer-matrix method. An exact ground-state phase diagram includes in total three unconventional quantum ground states with a quantum entanglement of the decorating spin-1 Heisenberg dimers apart from... |
We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain quenched disorder, whereas the structural glasses are here exemplified by the h... |
We develop an algorithmic, system-specific renormalization group (RG) procedure that is adapted from model reductions techniques from engineering control theory. The resulting "generalized" RG is a consistent generalization of the Wilsonian RG. |
We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to $\exp{({const} \beta)}$ in the Ising, $\sqrt{\beta}$ in the classical XY, and $\beta$ in the classical Heisenberg spin systems with... |
Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T -> 0), the size of the system going to... |
The chaotic hypothesis is proposed as a basis for a general theory of nonequilibrium stationary states. <br>Version 2: new comments added after presenting this talk at the Meeting mentioned in the Acknowledgement. |
We obtain the equations that define the equilibrium of a homogeneous relativistic gas of neutrons, protons and electrons in a constant magnetic field as applied to the conditions that probably occur near the center of neutron stars. We compute the relative densities of the particles at equilibrium and the Fermi moment... |
A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density matrix (stochastic series expansion), and avoids the interaction summations necessar... |
A general understanding of optimal control in non-equilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susce... |
Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the network of states. |
The Binder cumulant (BC) has been widely used for locating the phase transition point accurately in systems with thermal noise. In systems with quenched disorder, the BC may show subtle finite-size effects due to large sample-to-sample fluctuations. |
An ansatz applied to the two-dimensional Ising model in an external magnetic field h gives rise to an exactly soluble model. The singularity in the magnetization found by Onsager does not survive the presence of the external magnetic field as found earlier by Lee and Yang in 1952. |
Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates of the field variable (position vector r in real space or wavevector q in recip... |
Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating f... |
For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. Both for attractive and repulsive nearest-neighbor interactions among particles and for a wide range of paramete... |
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in nature is cooperative evolution. |
The short-range correlations are considered for a two-dimensional hard-core boson model on square lattice within Bethe approximation for the clusters consisting of two and four sites. Explicit equations are derived for the critical temperatures of charge and superfluid ordering and their solutions are considered for v... |
We study a coarse-grained model for a water monolayer that cannot crystallize due to the presence of confining interfaces, such as protein powders or inorganic surfaces. Using both Monte Carlo simulations and mean field calculations, we calculate three response functions: the isobaric specific heat $C_P$, the isotherm... |
In a nonequilibrium steady state, the violation of the fluctuation-dissipation theorem (FDT) is connected to breaking detailed balance. For the velocity correlations of a driven colloidal particle we calculate an explicit expression of the FDT violation. |
Firm foundation theory estimates a security's firm fundamental value based on four determinants: expected growth rate, expected dividend payout, the market interest rate and the degree of risk. In contrast, other views of decision-making in the stock market, using alternatives such as human psychology and behavior... |
We propose a method for calculating the isothermal critical exponent $\delta$ in Ising systems undergoing a second-order phase transition. It is based on the calculation of the mean magnetization time series within a small connected domain of a lattice after equilibrium is reached. |
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold... |
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally-relevant m... |
We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle eigenfunctions of the entanglement Hamiltonian are then seen to be spheroidal functions or generalizations of them. |
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