Chaos in the three-site Bose-Hubbard model -- classical vs quantum

TL;DR

This paper compares classical and quantum chaos in a three-site Bose-Hubbard model, revealing a strong correspondence between quantum measures and classical Lyapunov exponents, with unique multi-valued behavior of chaos indicators.

Contribution

It demonstrates the relationship between classical and quantum chaos measures in a mixed-behavior Bose-Hubbard system, highlighting novel multi-valued Lyapunov exponents.

Findings

Strong correlation between quantum eigenvalue statistics and classical Lyapunov exponents.

Largest Lyapunov exponent varies multi-valued with energy, unlike in purely chaotic or integrable systems.

Quantum measures of chaos align with classical chaos indicators across energy and interaction ranges.

Abstract

We consider a quantum many-body system - the Bose-Hubbard system on three sites - which has a classical limit, and which is neither strongly chaotic nor integrable but rather shows a mixture of the two types of behavior. We compare quantum measures of chaos (eigenvalue statistics and eigenvector structure) in the quantum system, with classical measures of chaos (Lyapunov exponents) in the corresponding classical system. As a function of energy and interaction strength, we demonstrate a strong overall correspondence between the two cases. In contrast to both strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multi-valued function of energy.