Quantum coherence controls the nature of equilibration in coupled chaotic systems

TL;DR

This paper investigates how quantum coherence influences the process of equilibration and thermalization in coupled chaotic quantum systems across different interaction regimes, revealing coherence as a key resource.

Contribution

It introduces a detailed analysis of quantum coherence's role in equilibration, identifying universal time scales and contrasting behaviors across perturbation strengths.

Findings

Maximally coherent states thermalize at all interaction strengths.

Entanglement growth is quadratic in ultra-weak regimes.

A universal time scale relates interaction strength to thermalization.

Abstract

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax towards an equilibrium. It is found that quantum coherence of the initial product states in the uncoupled eigenbasis can be viewed as a resource for equilibration and approach to thermalization as manifested by the entanglement. Results are given for four distinct perturbation strength regimes, the ultra-weak, weak, intermediate, and strong regimes. For each, three types of initially unentangled states are considered, coherent random-phase superpositions, random superpositions, and eigenstate products. A universal time scale is identified involving the interaction strength parameter. Maximally coherent initial states thermalize for any perturbation strength in spite of the fact that in the ultra-weak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. In contrast to the widespread linear behavior, in this regime the entanglement initially grows quadratically in time.