Metastability, chaos and spectrum tomography for Bose-Hubbard rings and chains

TL;DR

This paper investigates the metastability and spectral properties of Bose-Hubbard systems in finite rings and chains, linking quantum behavior to classical phase-space structures and analyzing chaos and localization.

Contribution

It introduces a semiclassical tomographic approach to connect many-body spectra with classical phase-space, exploring quantum ergodicity and chaos in Bose-Hubbard lattices.

Findings

Chaos diminishes as the system approaches the Gross-Pitaevskii limit.

Spectral analysis reveals the relation between classical dynamics and quantum metastability.

Both local (Bogoliubov) and global (chaotic) aspects are characterized.

Abstract

We analyze the metastability of Bose-Hubbard condensates for finite-size one-dimensional ring lattices and open chains, using a semiclassical tomographic perspective that emphasizes the relation of the many-body spectrum to the underlying classical phase-space structures. This constitutes an arena for inspection of quantum ergodicity and localization, in far-from-equilibrium scenarios of experimental interest. Both local aspects (via Bogoliubov analysis) and global aspects (by inspecting the mixed regular-chaotic dynamics) are addressed. We also clarify how chaos is diminished in the limit of the Gross-Pitaevskii equation.