Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion

TL;DR

This paper presents a systematic framework for deriving the effective Hamiltonian in non-Markovian open quantum systems, enabling analysis of energy shifts and eigenbasis changes due to environmental correlations, especially in strong-coupling regimes.

Contribution

It introduces a recursive perturbation expansion for the effective Hamiltonian, providing a new tool for analyzing non-Markovian dynamics and energy renormalization effects.

Findings

Environmental correlations influence energy shifts in spin systems.

The recursive expansion captures strong-coupling effects.

Framework aids understanding of non-Markovian quantum thermodynamics.

Abstract

We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to the time-local generator of the reduced dynamics. We derive a general expression for the effective Hamiltonian and develop a recursive perturbative expansion that expresses it in terms of system-bath interaction terms and bath correlation functions. This expansion provides a systematic tool for analyzing energy renormalization effects across different coupling regimes. Applying our framework to paradigmatic spin systems, we reveal how environmental correlations influence energy shifts and eigenbasis rotations, offering new insights into strong-coupling effects and non-Markovian quantum thermodynamics.