Correlation Decay and Markovianity in Open Systems

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 operation taken from large class, the uncoupled equilibrium state. We show that full system–reservoir dynamics given Markovian term plus correlation term, remainder small in coupling constant $$\lambda $$ uniformly for all times $$t\ge 0$$ The decays polynomially time, at speed independent of After this, becomes dominant, where evolves according completely positive, trace-preserving semigroup generated Davies generator, while stays stationary equilibrium. This shows (a) after initial correlations decay, enters regime both Born and Markov approximations valid, (b) reduced times, even correlated states.