Semiclassical quantization of the Bogoliubov spectrum

TL;DR

This paper uses semiclassical methods to analyze the Bogoliubov spectrum of a three-site Bose-Hubbard model, linking classical integrals of motion to quantum energy levels and identifying the transition to chaos.

Contribution

It introduces a semiclassical approach to connect classical integrals of motion with quantum spectra in the Bose-Hubbard model.

Findings

The Bogoliubov spectrum corresponds to the regular classical component.

Identified the full set of classical integrals of motion.

Determined the energy threshold for transition to chaos.

Abstract

We analyze the Bogoliubov spectrum of the 3-sites Bose-Hubbard model with finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motions of this regular component and, quantizing them, obtain the energy levels of the quantum system. The critical values of the energy, above which the regular Bogoliubov spectrum evolves into a chaotic spectrum, is indicated as well.