Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems

TL;DR

This paper presents a universal, self-consistent framework for describing velocity-dependent friction and diffusion in various systems including dusty plasmas, gases, and active biological particles, using Fokker-Planck and master equations.

Contribution

It develops a general description of velocity-dependent friction and diffusion coefficients, relates diffusion in coordinate and velocity spaces, and introduces a method to construct probability distributions without partial differentiation.

Findings

Identifies conditions for negative friction in plasmas.

Formulates a general equation for time-dependent probability transition functions.

Provides a unified approach applicable to passive and active particles.

Abstract

A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g., cells in biological systems) is suggested on the basis of the appropriate Fokker-Planck equation. Restrictions for application of the Fokker-Planck equation to the problem of velocity-dependent friction and diffusion coefficients are found. General description for this coefficient is formulated on the basis of master equation. Relation of the diffusion coefficient in the coordinate and velocity spaces is found for active (capable to transfer momentum to the ambient media) and passive particles in the framework of the Fokker-Planck equation. The problem of anomalous space diffusion is formulated on the basis of the appropriate probability transition (PT) function. The method of partial differentiation is avoided to construct the correct probability distributions for arbitrary distances, what is important for applications to different stochastic problems. Generale equation for time-dependent PT function is formulated and discussed. Generalized friction in the velocity space is determined and applied to describe the friction force itself as well as the drag force in the case of a non-zero driven ion velocity in plasmas. The negative friction due to ion scattering on grains exists and can be realized for the appropriate experimental conditions.