Phase space description of spin dynamics

The spin system with Hamiltonian (H) over cap (S) = -xi(S) over cap (Z) - sigma(S) over cap (2)(Z) (xi and sigma are external and internal field parameters) is treated as an example of the phase space description of spin dynamics using a master equation for the quasiprobability distribution function of spin orientations in the representation ( phase) space of the polar angles ( analogous to the Wigner phase space distribution for translational motion). The master equation yields ( via the Wigner-Stratonovich transformation of the density matrix) the solution as a Fourier series in the spherical harmonics with Fourier coefficients given by the statistical moments in a manner analogous to the classical distribution. The relaxation time of the longitudinal component of the spin can be estimated using a quantum generalization of the classical integral relaxation time via the stationary distribution and diffusion coefficient of the master equation.