Accelerated relaxation and Mpemba-like effect for operators in open quantum systems

TL;DR

This paper investigates the quantum Mpemba effect in open quantum systems, introducing a new operator distance measure to detect accelerated relaxation phenomena, and finds that genuine Mpemba-like effects occur in higher-dimensional systems and certain nonlocal operators.

Contribution

It develops a generalized framework using a dressed operator distance to identify Mpemba-like effects in non-trace preserving dynamics of open quantum systems, revealing effects in higher dimensions and nonlocal operators.

Findings

Only accelerated relaxation observed in single qubits.

Genuine Mpemba-like effects emerge in qutrits and higher systems.

Mpemba-like effects found in nonlocal operators like current.

Abstract

Quantum Mpemba effect occurs when a quantum system, residing far away from the steady state, relaxes faster than a relatively nearer state. We look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a non-trace preserving map, the trace distance of an operator is not a monotonically decaying function of time, unlike its quantum state counterpart. Consequently, the trace distance can not serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a \textit{dressed} distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. Applying the formalism to various open quantum system settings, we find that, interestingly, in the single qubit case, only accelerated relaxation of operators is possible, while genuine Mpemba-like effects emerge in higher-dimensional systems such as qutrits and beyond. Furthermore, we demonstrate the existence of Mpemba-like effects in nonlocal, non-equilibrium operators, such as current, in a double-quantum-dot setup. Our results, besides offering fundamental insight about the occurrence of the Mpemba-like effect under non-trace preserving dynamics, open avenues for new experimental studies where quicker relaxation of observables could be of significant interest.