Field induced stationary state for an accelerated tracer in a bath

TL;DR

This paper investigates the steady state behavior of an accelerated tracer particle in a bath, analyzing analytical solutions of a generalized Boltzmann-Lorentz equation and validating results with numerical simulations, focusing on diffusion and velocity distribution tails.

Contribution

It provides a comprehensive analytical framework for tracer dynamics under acceleration, including the cold bath limit, validated by multiple numerical methods.

Findings

Analytical solutions match numerical simulations across various methods.

Velocity distribution tails exhibit specific asymptotic behaviors.

Cold bath limit reveals unique tracer velocity characteristics.

Abstract

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.