Lectures

ABSTRACT

Understanding low-energy properties of the weakly interacting Bose gas has a long history in theoretical and mathematical physics. In 1947, assuming that the ground state exhibits Bose-Einstein condensation (BEC), Bogoliubov suggested a theory that provides expressions for the leading order contributions to the ground state energy and that predicts a linear excitation spectrum for dilute Bose gases in the thermodynamic limit.

In this course, I discuss recently developed methods with A. Adhikari, C. Boccato, M. Caporaletti, S. Cenatiempo, B. Schlein and S. Schraven to establish BEC and Bogoliubov’s energy predictions in the Gross-Pitaevskii scaling regime (and slightly beyond it). I conclude the lectures with some open questions related to the thermodynamic limit.

SCHEDULE