Irreversibility in Heisenberg Spin Systems. II. Approximate Solution of the High-Temperature Kinetic Equations

Abstract

A systematic approximation scheme is proposed that permits solution of the kinetic equations, recently derived by the authors, describing the high-temperature behavior of the spin autocorrelation function ${\Gamma }_{\mathrm{ab}}\mathrm{}\left(t\right)\mathrm{}$. A numerical solution and approximate analytical expressions are given in the first approximation and the importance of the neglected terms is discussed. It is shown that the direct autocorrelation function has an approximate Gaussian behavior for short times and decays then to zero through damped oscillations. A diffusion equation is derived for the short-wave-number Fourier components of ${\Gamma }_{\mathrm{ab}}\mathrm{}\left(t\right)\mathrm{}$. We also compare this theory with previous work on the subject.