Kramers equation for a charged Brownian particle: The exact solution

TL;DR

This paper derives the exact fundamental solution for Kramers equation describing charged Brownian particles in uniform external fields, enabling precise analysis of their long-term hydrothermodynamical behavior.

Contribution

It provides the first exact solution to Kramers equation for charged particles under arbitrary homogeneous external fields.

Findings

Exact fundamental solution derived

Application to hydrothermodynamics in long time regime

Enhanced understanding of charged particle dynamics

Abstract

We report the exact fundamental solution for Kramers equation associated to a brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic fields. Some applications are presented, namely the hydrothermodynamical picture for Brownian motion in the long time regime.