Multiple quantum Mpemba effect: exceptional points and oscillations

TL;DR

This paper investigates how exceptional points and complex eigenvalues influence the occurrence of multiple quantum Mpemba effects in a driven dissipative two-level quantum system, revealing conditions for multiple observable crossings during relaxation.

Contribution

It introduces the concept of multiple quantum Mpemba effects arising from exceptional points and complex eigenvalues, with analytical results for density matrix evolution including coherence effects.

Findings

Multiple quantum Mpemba effects can occur due to exceptional points and complex eigenvalues.

Observables like energy and entropy can exhibit single or multiple Mpemba effects depending on parameters.

Distance from steady state in Kullback-Leibler divergence shows only a single Mpemba effect.

Abstract

We explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect. To this end, we study a two-level driven dissipative system subjected to an oscillatory electric field and dissipative coupling with the environment. We find that both exceptional points and complex eigenvalues can lead to $multiple$ quantum Mpemba effect. It occurs in an observable when time evolved copies corresponding to two different initial conditions, one initially having higher observable value compared to the other and both relaxing towards the same steady state, intersect each other more than once during their relaxation process. Each of the intersections denotes a quantum Mpemba effect and marks the reversal of identities between the two copies i.e. the copy with higher observable value before the intersection becomes the lower valued copy (and vice versa) after the intersection. Such multiple intersections originate from additional algebraic time dependence at the exceptional points and due to oscillatory relaxation in the case of complex eigenvalues. We provide analytical results for quantum Mpemba effect in the density matrix in presence of coherence. Depending on the control parameters (drive and dissipation), observables such as energy, von Neumann entropy, temperature etc. exhibit either single or multiple quantum Mpemba effect. However, the distance from steady state measured in terms of the Kullback-Leibler divergence shows only single quantum Mpemba effect although the corresponding speed gives rise to either single or multiple quantum Mpemba effect.