On the spherical symmetry and finite-range assumptions of the interaction potential in the low energy study of dilute Bose gases

Abstract

We consider a Bose gas on the three-dimensional torus in the Gross--Pitaevskii regime and explain how to remove the assumptions of radiality and compact support on the interaction potential in the proof of Bose--Einstein condensation and convergence of the excitation spectrum to Bogoliubov's prediction. In particular, we sketch the proof of [50].