Expedited thermalization dynamics in incommensurate systems

TL;DR

This paper investigates how incommensurate quantum systems coupled to a thermal bath rapidly reach an infinite-temperature state, with localized and cold initial states relaxing faster, revealing complex thermalization behaviors influenced by disorder and dissipation.

Contribution

It uncovers the accelerated thermalization of localized and low-temperature states in incommensurate systems due to environmental dissipation, linking disorder, initial conditions, and relaxation dynamics.

Findings

Localized states relax faster than delocalized states.

Low-temperature initial states thermalize more rapidly than high-temperature ones.

The slowest Liouvillian mode governs the expedited thermalization process.

Abstract

We study the thermalization dynamics of a quantum system embedded in an incommensurate potential and coupled to a Markovian thermal reservoir. The dephasing induced by the bath drives the system toward an infinite-temperature steady state, erasing all initial information-including signatures of localization. We find that initially localized states can relax to the homogeneous steady state faster than delocalized states. Moreover, low-temperature initial states thermalize to infinite temperature more rapidly than high-temperature states -- a phenomenon reminiscent of the Mpemba effect, in which hotter liquids freeze faster than colder ones. The slowest relaxation mode in the Liouvillian spectrum plays a critical role in the expedited thermalization for localized or cold initial states. Our results reveal that the combination of disordered structure and environmental dissipation may lead to non-trivial thermalization behavior, which advances both the conceptual framework of the Mpemba effect and the theoretical understanding of nonequilibrium processes in dissipative disordered systems.