Interacting bosons in a triple well: Preface of many-body quantum chaos

TL;DR

This paper investigates how a system of interacting bosons in a triple-well potential transitions to quantum chaos as it becomes less integrable, revealing features of chaos and near-integrability in its spectral and eigenstate properties.

Contribution

It provides a systematic analysis of quantum chaos onset in a three-site bosonic system using spectral statistics and eigenstate structure, highlighting the transition from integrability to chaos.

Findings

Eigenstates are near-chaotic, showing non-Gaussian distributions.

Spectral measures indicate a transition towards chaos with potential tilt.

Observable properties reflect the system's proximity to integrability.

Abstract

Systems of interacting bosons in triple-well potentials are of significant theoretical and experimental interest. They are explored in contexts that range from quantum phase transitions and quantum dynamics to semiclassical analysis. Here, we systematically investigate the onset of quantum chaos in a triple-well model that moves away from integrability as its potential gets tilted. Even in its deepest chaotic regime, the system presents features reminiscent of integrability. Our studies are based on level spacing distribution and spectral form factor, structure of the eigenstates, diagonal and off-diagonal elements of observables in relationship to the eigenstate thermalization hypothesis. With only three sites, the system's eigenstates are at the brink of becoming fully chaotic and thus show distributions other than Gaussian, which resonates with the results for the observables.