Conditions for the validity of the quantum Langevin equation

Abstract

From microscopic models, a Langevin equation can in general be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of `slow' variables. We test this method by comparison with an exactly soluble model, and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevn equation as an intermediate step.