A path integral theory of relaxation I

Abstract

A path integral relaxation theory is given for bason and spin systems. A relevant system is considered to be in contact with its reservoir. A (quasi-)probability density is written in the form of path integrals over system and reservoir variables. The system variables are eliminated with the aid of coherent states, yielding simple path integral formulas for the probability density and an average value of system operators written in terms of the reservoir variables only. These expressions are valid for any kind of reservoir (stochastic) variables including the Markoffian process as a special case. A method of evaluating the path integrals in the time domain is briefly discussed. As an illustrative example, time evolution of the probability density is explicitly calculated for a model of random frequency modulation. For the Markoffian process, the path integrals can be calculated analytically and it is shown that the absorption spectrum reduces to a simpler form.