Non-Markovian quantum dynamics from environmental relaxation

We consider the dynamics of composite quantum systems in the particular case that the state operator relaxes towards the Born approximation. For this we augment the von Neumann equation by a relaxation operator imposing a finite relaxation time τr . Under the premise that the relaxation is the dominant process we obtain a hierarchy of non-Markovian master equations. The latter arises from an expansion of the total state operator in powers of the relaxation time τr . In the Born-Markov limit τr → 0 the Lindblad master equation is recovered. Higher-order contributions enable a systematic treatment of correlations and non-Markovian dynamics in a recursive manner.