  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.
