On the quantum statistical theory of relaxation in isolated spin systems

Abstract

The long time approach to statistical equilibrium of a spin system, isolated from the lattice vibrations, is studied, starting from the relaxation function of Kubo and Tomita. Only the behaviour of the longitudinal magnetization is considered. The formalism used is based on the fact that in general a coarse grained description of the behaviour of macroscopic variables is sufficient. For this purpose quantum-mechanical phase cells are introduced, which are characterized by the macro energy and the longitudinal magnetization.

It is derived that in terms of these phase cells the asymptotic behaviour of the system is described by a first order differential equation, the so-called master equation. From this derivation the important condition follows that this master equation is only valid in the presence of either a large magnetic field or a strong exchange interaction between the spins. In investigating the relaxation function with the aid of the master equation use is also made of a linearity condition, which implies that the system is not far from statistical equilibrium. The result for the spin-spin relaxation time, computed in this way, disagrees with that of Caspers, but is the same as found by Hartmann and Anderson. Finally the theories of these authors on spin-spin relaxation are discussed.