Correlation Decay and Markovianity in Open Systems

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, uniformly for all times. The correlation term decays polynomially in time. 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.