English

Conditions for the validity of the quantum Langevin equation

Statistical Mechanics 2015-05-30 v1 Other Condensed Matter

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.

Keywords

Cite

@article{arxiv.1109.4840,
  title  = {Conditions for the validity of the quantum Langevin equation},
  author = {J. Frenkel and J. C. Taylor},
  journal= {arXiv preprint arXiv:1109.4840},
  year   = {2015}
}