Chaotic and regular dynamics in the three-site Bose-Hubbard model

TL;DR

This paper investigates the energy spectrum of the three-site Bose-Hubbard model, revealing a mixture of regular and chaotic dynamics, and uses statistical methods to analyze the spectral properties.

Contribution

It introduces a pseudoclassical approach to quantify regular and chaotic components in the spectrum and applies Berry-Robnik distribution for spectral analysis.

Findings

Spectrum contains both regular and chaotic components.

Good agreement between theoretical distribution and numerical data.

Quantitative measure of regular and chaotic volume fractions.

Abstract

We analyze the energy spectrum of the three-site Bose-Hubbard model. It is shown that this spectrum is a mixture of the regular and irregular spectra associated with the regular and chaotic components of the classical Bose-Hubbard model. We find relative volumes of these components by using the pseudoclassical approach. Substituting these values in the Berry-Robnik distribution for the level spacing statistics we obtain good agreement with the numerical data.