Bogoliubov excitation spectrum for Bose-Einstein condensates

Abstract

We consider interacting Bose gases trapped in a box $Λ= [0;1]^3$ in the Gross-Pitaevskii limit. Assuming the potential to be weak enough, we establish the validity of Bogoliubov's prediction for the ground state energy and the low-energy excitation spectrum. These notes are based on \cite{BBCS3}, a joint work with C. Boccato, C. Brennecke and S. Cenatiempo.

18 pages. Contribution to Proceedings of the International Congress of Mathematicians, Rio de Janeiro, 2018