2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23765We 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.minor change, 4 pages, 4 figures, to appear in Phys. Rev. LettSoft Condensed MatterStatistical MechanicsChaotic DynamicsQuantum Physicstext