Correlation decay and Markovianity in open systems

TL;DR

This paper demonstrates that in open quantum systems, initial correlations decay polynomially over time, leading to a Markovian regime where the system's evolution is well-described by a Davies generator, valid for all times.

Contribution

It proves that the dynamics of a coupled quantum system and reservoir becomes effectively Markovian after initial correlations decay, even when starting from correlated states.

Findings

Correlation term decays polynomially in time

Markovian dynamics dominate after initial decay

System evolution follows Davies generator for all times

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.