Related papers: Spatial distributions of non-conservatively intera…
The standard relationships of statistical mechanics are upended my the presence of active forces. In particular, it is no longer usually possible to simply write down what the stationary probability of a state of such a system will be, as…
We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate…
The purpose of this paper is to study the evolution of moving interacting particles on the mesoscopic scale. We will introduce an uncertainty principle and a new priori bound for the evolution of particles subject to a general mesoscopic…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…
Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…
We describe, at the microscopic level, the dynamics of N interacting components where the probability is very small when N is large that a given component interact more than once, directly or indirectly, up to time t, with any other…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…
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…
We analyse the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer et al., Phys. Rev. Lett. 103, 210401 (2009), we unveil a fundamental connection…
We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensionnal model of active particles. We…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
We study the dynamics of inertial active particles in a one-dimensional chain with harmonic nearest-neighbor interactions, highlighting the interplay of persistence, interaction, and inertial timescales. Using a Green's function approach,…
We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…