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Physics

Exploring Quantum Mpemba Effects

Ulrich Warring

Published Jul 1, 2024• 6 citations
Publisher
DOI
10.1103/physics.17.105

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Relaxation towards equilibrium is often assumed to be slower when a system starts farther from equilibrium, but this intuition fails in the Mpemba effect. Recent advances in controllable quantum platforms have enabled the exploration of its quantum analogue, the quantum Mpemba effect (QME), yet its microscopic origin remains largely unclear. Here we provide a general framework for understanding the QME in closed quantum many-body chaotic systems by reformulating the equilibration process of local subsystems in terms of Ruelle-Pollicott (RP) resonances. We show that suppressing the initial-state overlap with the dominant RP resonant mode accelerates subsystem equilibration and thereby yields the QME. We further uncover that a novel type of strong QME can occur via complete translation-symmetry breaking of initial states. We substantiate our predictions using the prototypical kicked Ising chain and a quantum automaton circuit. These findings cast the QME in closed many-body systems into a unified framework with open-system analogues and provide experimentally accessible signatures on state-of-the-art quantum platforms.
We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global U ( 1 ) symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional diagnostics such as the trace distance, while offering a complementary interpretation in terms of Hilbert-space exploration and dynamical delocalization. In U ( 1 ) -symmetric systems, we confirm that the recently proposed symmetric component of Krylov complexity serves as a robust and reliable indicator of the quantum Mpemba effect, capturing anomalous relaxation even in cases where the total complexity fails to do so.