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

TL;DR

This paper derives approximate expressions for the Hamiltonian of mean force in quantum systems under weak coupling and high-temperature conditions, improving quantum master equations for better accuracy.

Contribution

It introduces perturbative formulas for the Hamiltonian of mean force and demonstrates how replacing the system Hamiltonian enhances the Bloch-Redfield master equation.

Findings

Approximate Hamiltonians of mean force derived for weak coupling and high temperature.

Numerical analysis confirms improved accuracy of master equations with the new Hamiltonians.

Enhanced precision of quantum dynamics modeling in non-negligible system-bath interactions.

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.