Theory of Relaxation in a Group of Weakly Coupled Systems

Abstract

A general formalism for computing relaxation times characterizing two or more weakly coupled macroscopic systems is presented. The physical nature of the systems is arbitrary, although applications to spin systems are briefly discussed. The main assumptions are that each system is internally in equilibrium with a well-defined temperature, that the systems are weakly coupled to one another, and that the Hamiltonians of the systems form a commuting set. No high-temperature approximations are used. The formalism is presented in an effort to unify in part the approaches which have been developed for many special physical situations, and to show the form some relaxation times take when the high-temperature approximations are not used. It is shown that when one of two coupled systems is a "Zeeman" system, the (spin) relaxation time is proportional to the magnetic adiabatic susceptibility.