Theory of Relaxation of a Two-Spin System

The relaxation of a system of two inequivalent spins ($S=\frac{1}{2}$, $I=\frac{1}{2}$) with two noncommuting time-dependent interactions, i.e., a randomly modulated dipole interaction, and a fluctuating local field acting on one of the spins ($S$), is discussed. The influence of the fluctuating field is treated exactly in terms of a Fokker-Planck equation, which is described in the previous paper. The dipole interaction is then treated with perturbation theory. This gives, in all detail, the time-dependent transitions between the levels established in a constant external field. It is shown that rate equations are insufficient to describe the transitions, and that in weak fields a resonance phenomenon can occur. This resonance is studied in some detail with Green's function methods.