Dynamics of Open Quantum Systems II, Markovian Approximation

Abstract

A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperatureT>0. We show that for fixed, small values of the coupling constantλ, the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics isO(|λ|1/4)for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracyO(|λ|1/4)for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as1/t4or faster, which is a significant improvement relative to the previously required exponential decay.