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.

22 pages; 4 figures

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Cited by in corpus (14)

• Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
• Strong coupling non-Markovian quantum thermodynamics of a finite-bath system
• Steady state in ultrastrong coupling regime: perturbative expansion and first orders
• Corrections to the Hamiltonian induced by finite-strength coupling to the environment
• Energy measurements remain thermometrically optimal beyond weak coupling
• Page-curve-like entanglement dynamics in open quantum systems
• Stochastic simulation of dissipative quantum oscillators
• Structure of the Hamiltonian of mean force
• Global becomes local: Efficient many-body dynamics for global master equations
• Potential renormalisation, Lamb shift and mean-force Gibbs state -- to shift or not to shift?
• Open system dynamics in interacting quantum field theories
• Quantum Thermodynamics of Open Quantum Systems: Nature of Thermal Fluctuations
• Quantifying spectral signatures of non-Markovianity beyond the Born-Redfield master equation
• Structure of Quantum Mean Force Gibbs States for Coupled Harmonic Systems