Exponentially accelerated relaxation and quantum Mpemba effect in open quantum systems

TL;DR

This paper demonstrates how to accelerate relaxation in open quantum systems using permutation-based transformations, revealing a quantum Mpemba effect where systems farther from equilibrium can relax faster, with broad applicability.

Contribution

It introduces a class of permutation-based protocols to induce the quantum Mpemba effect, accelerating convergence to equilibrium in open quantum systems.

Findings

Permutation matrices can suppress slowest decay modes.

Quantum Mpemba effect observed in various distances and models.

Protocol is computationally efficient and broadly applicable.

Abstract

We investigate the quantum Mpemba effect in the relaxation of open quantum systems whose effective dynamics is described by Davies maps. We present a class of unitary transformations built from permutation matrices that, when applied to the initial state of the system, (i) suppress the slowest decaying modes of the nonunitary dynamics; (ii) maximize its distinguishability from the steady state. The first requirement guarantees exponentially accelerating convergence to the steady state, and the second implies that a quantum system initially farther from equilibrium approaches it more rapidly than one that starts closer. This protocol provides a genuine Mpemba effect, and its numerical simulation requires low computational effort. We prove that, for any initial state, one can always find a permutation matrix that maximizes its distance from equilibrium for a specified information-theoretic distinguishability measure. We illustrate our findings for a two-level system, and also for the nonunitary dynamics of the transverse field Ising chain and XXZ chain, each weakly coupled to a bosonic thermal bath, and demonstrate the quantum Mpemba effect as captured by the Hilbert-Schmidt distance, quantum relative entropy, and trace distance. Our results provide a versatile framework to engineer the genuine quantum Mpemba effect in Markovian open quantum systems.