Stochastic model for the dynamics of a spin-oscillator coupled system

For a model system consisting of bilinearly coupled harmonic oscillators and pseudospins, a generalized Langevin equation for the oscillator subsystem, valid for general spatial dimensionality and interaction range, is derived exactly, using Mori's projection operator technique. The retarded friction kernel is derived to second order in the spinoscillator interaction constant. It is shown that for a one-dimensional model system treated in an earlier paper, the oscillator susceptibility predicted by this approximation, is identical to the susceptibility obtained then by a phenomenological Langevin equation approach.