We deduce a class of non-Markovian completely positive master equations which describe a system in a composite bipartite environment, consisting of a Markovian reservoir and additional stationary unobserved degrees of freedom that modulate the dissipative coupling. The entanglement-induced memory effects can persist for arbitrary long times and affect the relaxation to equilibrium, as well as induce corrections to the quantum-regression theorem. By considering the extra degrees of freedom as a discrete manifold of energy levels, strong non-exponential behaviour can arise, such as for example power law and stretched exponential decays.
The final, definitive version of this article has been published in the Journal, Journal of Physics A 38 (42), 2005, © Institute of Physics