Correlation decay and Markovianity in open systems

• URL: http://arxiv.org/abs/2107.02515v2
• Date: Wed, 10 Aug 2022 12:35:18 GMT
• Title: Correlation decay and Markovianity in open systems
• Authors: Marco Merkli
• Abstract summary: We show that the full system-reservoir dynamics is given by a markovian term plus a correlation term. The correlation term decays in time, at a speed independent of $lambda$. This shows that (a) after initial SR correlations decay, the SR dynamics enters a regime where both the Born and Markov approximations are valid, and (b) the reduced system dynamics is markovian for all times.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A finite quantum system S is coupled to a thermal, bosonic reservoir R. Initial SR states are possibly correlated, obtained by applying a quantum operation taken from a large class, to the uncoupled equilibrium state. We show that the full system-reservoir dynamics is given by a markovian term plus a correlation term, plus a remainder small in the coupling constant $\lambda$ uniformly for all times $t\ge 0$. The correlation term decays polynomially in time, at a speed independent of $\lambda$. After this, the markovian term becomes dominant, where the system evolves according to the completely positive, trace-preserving semigroup generated by the Davies generator, while the reservoir stays stationary in equilibrium. This shows that (a) after initial SR correlations decay, the SR dynamics enters a regime where both the Born and Markov approximations are valid, and (b) the reduced system dynamics is markovian for all times, even for correlated SR initial states.

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