Generalized Phase-Space Method in the Langevin-Equation Approach
Fumiaki Shibata, Natsuki Hashitsume
In this article is proposed a method of constructing the quantal Boltzmann-Langevin equation, i.e. the stochastic kinetic equation for a suitably chosen statistical operator with a fluctuating force term. This method is based on the use of the generalized phase-space method, which makes calculations very simple. As an example, the method of spin coherent states is applied to a model of a localized single spin placed under actions of its magnetic environment, and the Bloch-Langevin equation, i.e. the well-known Bloch equation for a spin magnetic moment with a fluctuating force term, is derived. The drift and the relaxation terms contained in the Boltzmann-Langevin and the Bloch-Langevin equations are completely in agreement with those previously obtained. An expression of the fluctuation-dissipation theorem generalized so as to include non-linear dissipation terms is given.
Journal of the Physical Society of Japan•May 1, 1978•38 citations