Christian Brennecke: Bogoliubov Theory in the Gross-Pitaevskii Limit

We consider Bose gases consisting of N particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order N−1(Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as N→∞, confirming Bogoliubov’s predictions.

In the talk, I will present the general strategy of our proof and explain in particular how to remove our previous assumption of small interaction potential, recently obtained in arXiv:1812.03086. This is joint work with C. Boccato, S. Cenatiempo and B. Schlein.