Brownian motion in a bath responding to external electric fields

Abstract

The Brownian motion of a charged particle immersed in a medium of charged particles is considered when the system is placed in electric fields. Coming from the Zwanzig-Caldeira-Legget particle-bath model, we modify it so that not only the Brownian particle (BP) but also the bath particles respond to the external fields. The generalized Langevin equation is derived for stationary systems. Arbitrarily time-dependent electric fields do not affect the memory function, the thermal noise force, and the BP velocity correlation function. Despite the effect of the external field on the bath particles, Kubo's second fluctuation-dissipation theorem remains unchanged. A general equation for the mean velocity of the BP, which is affected by the bath particles' response to the electric field, is obtained and solved for the Drude model of the frequency distribution of the bath oscillators.