Chaos, thermalization and breakdown of quantum-classical correspondence in a collective many-body system

TL;DR

This paper explores how quantum and classical dynamics align or diverge in a four-site Bose-Hubbard model, revealing three regimes with varying correspondence and unexpected slow convergence to classical behavior.

Contribution

It identifies three dynamical regimes in a collective many-body system and uncovers slow quantum-classical convergence due to finite-size effects.

Findings

Three dynamical regimes with different quantum-classical correspondence

Classical intermittency contrasts with quantum trapping in symmetry sectors

Slow convergence to classical limit indicates strong finite-size effects

Abstract

We investigate thermalization and the quantum-classical correspondence in the collective Bose-Hubbard model, focusing on the four-site case. Our analysis of the classical phase-space structure and its excited-state quantum phase transitions leads us to three dynamical regimes: symmetry-breaking low-energy states, an intermediate region where quantum and classical equilibrium states markedly disagree, and a high-energy regime with restored correspondence. The observed classical intermittency above the first excited-state quantum phase transition contrasts with quantum dynamics, which remains trapped in symmetry-breaking sectors despite the existence of a classically connected phase. This mismatch originates from the population of imbalance-carrying eigenstates and persists even for relatively large number of particles. Our results reveal unexpectedly slow convergence to the classical limit, signaling robust finite-size effects in collective many-body dynamics.