Related papers: On statistics and 1/f noise of molecular random wa…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
A formally exact relation is derived which connects thermodynamically non-equilibrium evolution of gas density distribution after its arbitrary strong spatially non-uniform perturbation and evolution of many-particle correlations between…
The BBGKY hierarchy of equations for a particle interacting with an ideal gas is investigated. Principal properties of its solutions are disclosed, as exact identities which connect probability distribution of path of the particle, its…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The…
We study the relaxation of a test particle immersed in a bath of field particles interacting via weak long-range forces. To order 1/N in the $N\to +\infty$ limit, the velocity distribution of the test particle satisfies a Fokker-Planck…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
We present a molecular dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short distance correlations in the non-equilibrium…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
Diffusivity in some soft matter and biological systems changes with time, called the fluctuating diffusivity. In this work, we propose a novel origin for fluctuating diffusivity based on stochastic simulations of binary gas mixtures. In…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…
We present molecular dynamics simulations of a binary Lennard-Jones mixture at temperatures below the kinetic glass transition. The ``mobility'' of a particle is characterized by the amplitude of its fluctuation around its average position.…
We study the heterogeneous dynamics of attractive colloidal particles close to the gel transition using confocal microscopy experiments combined with a theoretical statistical analysis. We focus on single particle dynamics and show that the…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the…
We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a…
The 1/f-noise is considered which has no relation to long-lasting processes but originates from the same dynamical mechanisms as what are responsible for the loss of memory, fast relaxation and usual shot noise. The universal long-range…
An impact of particles' roughness on the self-diffusion coefficient in granular gases is investigated. For a simplified collision model where the normal and tangential restitution coefficients are assumed to be constant we develop an…