Correlation Decay and Markovianity in Open Systems

Abstract

A finite quantum system $$\mathrm{S}$$ is coupled to a thermal, bosonic reservoir $$\mathrm{R}$$ . Initial $$\mathrm{S}\mathrm{R}$$ 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 $$\mathrm{S}\mathrm{R}$$ correlations decay, the $$\mathrm{S}\mathrm{R}$$ 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 $$\mathrm{S}\mathrm{R}$$ initial states.