On the generalized Langevin equation: Classical and quantum mechanicala)

Abstract

The generalized Langevin equation and its attendant fluctuation–dissipation relation (FDR) for both classical and quantum systems is explictly derived for a large class of system-bath interaction potentials. We demonstrate for this class of potentials that the classical FDR involving only the temperature of the bath is satisfied, and that in general the decay times of the dissipative processes and of the system are temperature dependent. We also demonstrate that the quantum FDR depends in detail on the nature of the bath and on the specific system-bath interaction. Thus we conclude that while the classical Langevin equation is phenomenologically useful, its quantum counterpart is much more limited.