Speaker
Description
The Brownian motion of a particle in a bath of other particles is effectively described by the
generalized Langevin equation (GLE). Following Kubo, it is usually assumed that if external
forces act on the system, they do not affect the thermal force and the memory function that
enter the GLE. The action of such forces is restricted to the Brownian particle (BP), leaving
the bath particles unaffected by the external field. However, there are many physical
situations, when not only the BP but also the bath particles are subjected to the external field.
We show that for stationary systems in a harmonic potential the corresponding generalization
of the Zwanzig-Caldeira-Legget theory leads to the GLE for which Kubo’s fluctuation-
dissipation theorem remains valid but both the memory function and the thermal force depend
on the elastic constant of the confinement potential. As a result, the correlation functions
describing the random motion of the BPs change in comparison with those in the original
model as well. We discuss possibilities to calculate these functions and show several specific
solutions for them depending on the frequency distribution of the bath oscillators and the
coupling between the bath and the BP.
