Quantum Chaos of Bogoliubov Waves for a Bose-Einstein Condensate in Stadium Billiards

TL;DR

This paper explores quantum chaos in Bogoliubov excitations of a Bose-Einstein condensate within stadium billiards, predicting that their level spacing statistics mirror those of non-interacting systems despite mean field interactions.

Contribution

It demonstrates that the level spacing distribution of Bogoliubov excitations remains unchanged by mean field interactions, through a mapping to a real symmetric matrix and numerical validation.

Findings

Level spacing distribution matches non-interacting systems

Mapping non-Hermitian to real symmetric matrices is effective

Numerical tests confirm theoretical predictions

Abstract

We investigate the possibility of quantum (or wave) chaos for the Bogoliubov excitations of a Bose-Einstein condensate in billiards. Because of the mean field interaction in the condensate, the Bogoliubov excitations are very different from the single particle excitations in a non-interacting system. Nevertheless, we predict that the statistical distribution of level spacings is unchanged by mapping the non-Hermitian Bogoliubov operator to a real symmetric matrix. We numerically test our prediction by using a phase shift method for calculating the excitation energies.