Non-Markovian relaxation of a spin-1/2 particle in a fluctuating transverse field: Cumulant expansion and stochastic simulation results

We consider the relaxation dynamics of a spin-1/2 particle in a fluctuating transverse magnetic field. With a cumulant expansion technique (up to sixth order) we calculate the time dependence of the approach to equilibrium of the population difference of the two spin levels and of the phase coherence. We find that for intermediate strength coupling to the fluctuations, the cumulant expansion converges, and the relaxation to equilibrium can have a pronounced non-Markovian character. We compare these analytic results with numerically exact data from stochastic simulations.