Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations

Abstract

The Hamiltonian of mean force is a widely used concept to describe the modification of the usual canonical Gibbs state for a quantum system whose coupling strength with the thermal bath is non-negligible. Here we perturbatively derive general approximate expressions for the Hamiltonians of mean force in the weak-coupling approximation and in the high-temperature one. We numerically analyse the accuracy of the corresponding expressions and show that the precision of the Bloch-Redfield equantum master equation can be improved if we replace the original system Hamiltonian by the Hamiltonian of mean force.

Canonically consistent quantum master equation

“…Despite the lack of CP, a stringent restriction for physical maps [23,39], the Redfield equation is able to capture finite system-bath coupling effects for which the Lindblad is insensitive [26,40]. Thus, it is only recently that the Redfield equation has gained popularity as a tool to incorporate finite systembath coupling effects [27,34,35,[41][42][43]. To this goal, we propose below a scheme that uses the generalized Gibbs state from equilibrium statistical mechanics [28,29,33] to correct the Redfield QME, specifically improving on the approximation in Eq.…”