Master Langevin equations: Origin of asymptotic diffusion

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Abstract
We extend the master-equation treatment of dynamical evolution of a system-plus-reservoir configuration including the propagation of initial correlations as a noise source. Specializing into the quantum harmonic oscillator coupled to a fermionic heat bath, we develop a model for the diffusion matrix in the space of diagonal density operators. It can be shown that mean values of observables undergo Langevin-like motion and, in particular, that the mean value and dispersion of the oscillator quanta approach the canonical equilibrium values. A final interpretation of the characteristics and role of the noise source is given.