Geometry and restoration of the quantum Mpemba effect beyond weak-coupling regime in the spin-boson model

TL;DR

This paper explores the quantum Mpemba effect in the spin-boson model, revealing how system-bath coupling strength and distance measures influence the relaxation dynamics and geometric structure of the effect.

Contribution

It demonstrates the impact of coupling strength beyond weak-coupling regimes and uncovers geometric structures on the Bloch sphere related to the quantum Mpemba effect.

Findings

The effect depends on the distance measure used at low temperatures.

Increasing coupling enhances the effect in trace distance and restores it in quantum relative entropy.

A geometric structure on the Bloch sphere explains relaxation-order inversion.

Abstract

Understanding relaxation dynamics in open quantum systems is a central problem in nonequilibrium quantum physics. Here we investigate the quantum Mpemba effect in the spin-boson model. In the weak-coupling Markovian regime we show that the occurrence of the effect strongly depends on the choice of distance measure at low temperature: while it appears in the trace distance, it can disappear in the quantum relative entropy. Going beyond the weak-coupling approximation, numerically exact simulations of the full system-bath dynamics reveal that increasing coupling enhances the effect in the trace distance and restores it in the quantum relative entropy. For all spin-bath couplings prior to delocalized-localized quantum phase transition, we uncover a simple geometric structure of the effect on the Bloch sphere: within the excited-state hemisphere, pairs of states related by rotations generically exhibit relaxation-order inversion. These results highlight the role of geometry and system-environment correlations in anomalous quantum relaxation.