Related papers: Stochastic representation of deterministic interac…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
Bipartite matching systems arise in many settings where agents or tasks from two distinct sets must be paired dynamically under compatibility constraints. We consider a high-dimensional bipartite matching system under uncertainty and seek…
Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We use the stochastic quantization method to construct a supersymmetric version of the quantum spherical model. This is based on the equivalence between the Brownian motion described by a Langevin equation and the supersymmetric quantum…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
We consider the linear and quadratic higher order terms associated to the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the…
Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the…