Dynamics of Open Quantum Systems II, Markovian Approximation

TL;DR

This paper demonstrates that for small coupling, the dynamics of a finite quantum system coupled to a thermal bath can be accurately approximated by a Markovian semigroup, with an error of order ||^{1/4} for all times.

Contribution

It establishes a rigorous approximation of true quantum dynamics by Markovian semigroups with improved decay conditions on the reservoir correlations.

Findings

The Markovian approximation holds with an error of O(||^{1/4}) for all times.

Applicable to reservoirs with correlation decay as 1/t^4 or faster.

Provides a method based on a new expansion of the full system-bath propagator.

Abstract

A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature $T>0$. We show that for fixed, small values of the coupling constant $\lambda$, 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 is $O(|\lambda|^{1/4})$ for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy $O(|\lambda|^{1/4})$ 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 as $1/t^{4}$ or faster, which is a significant improvement relative to the previously required exponential decay.