Quantum Markovian master equations: resonance theory shows validity for all time scales

Abstract

Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum sciences. The accuracy of the master equation approximation was so far proven for small values of the system-environment interaction coupling strength $\lambda$, under the additional constraint that time $t$ must not exceed an upper bound, ${\lambda }^{2}t\le$ constant. Here, we show that the Markov approximation is valid for fixed small coupling strength and for all times. We also construct a new approximate Markovian dynamics -- a completely positive, trace preserving semigroup -- which is asymptotically in time exact, to all orders in the coupling.

Version published in journal (Ann. Phys. 2020); title slightly changed w.r.t. arXiv V1 (referee request), but same as journal version, some references added

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