Related papers: Field theories and exact stochastic equations for …
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
We introduce a stochastic equation for the microscopic motion of a tagged particle in the single file model. This equation provides a compact representation of several of the system's properties such as Fluctuation-Dissipation and Linear…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle $i$ carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
We consider a stochastic differential equation for a charged particle in a stochastic magnetic field, known as A-Langevin equation. The solution of the equation is found, and the Lagrange velocity correlation function is calculated in…
The Langevin equation is ubiquitously employed to numerically simulate plasmas, colloids and electrolytes. However, the usual assumption of white noise becomes untenable when the system is subject to an external AC electric field. This is…
We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the…
Relativistic effects in the thermodynamical properties of interacting particle systems are investigated within the framework of the relativistic direct interaction theory in various forms of dynamics. In the front form of relativistic…
We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the…
We introduce a fundamental theory for the kinetics of systems of classical particles. The theory represents a unification of kinetic theory, Brownian motion and field theory. It is self-consistent and is the dynamic generalization of the…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
The physics of particle acceleration in turbulent plasmas is a topic of broad interest, which is making rapid progress thanks to dedicated, large-scale numerical experiments. The first part of this paper presents an effective theory of…
Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An…
Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…