Bloch sphere picture and restoration of the quantum Mpemba effect beyond the weak coupling regime in the spin boson model

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. We uncover a simple Bloch sphere picture of the effect: within the excited-state hemisphere, pairs of states related by rotations and having the same Bloch-vector modulus generically exhibit an inversion of their relaxation ordering. This behavior is robust across sub Ohmic, Ohmic, and super Ohmic bath spectra. In the Ohmic and sub Ohmic regimes, the crossing time becomes strongly suppressed upon approaching the critical region, whereas in the super Ohmic regime the effect remains enhanced despite the absence of a finite-coupling localization transition. These results highlight the interplay between geometry, distance measures, system--environment coupling, and bath spectral properties in anomalous quantum relaxation.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2603.17565 [quant-ph]

(or arXiv:2603.17565v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.17565 Focus to learn more arXiv-issued DOI via DataCite

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