Appears in collection : Large-scale limits of interacting particle systems

We consider systems of N interacting bosons in the Gross-Pitaevskii limit, where both the range and the scattering length of the potential are of the order 1/N, and N tends to infinity. We present recent tools allowing to determine the low-energy spectrum up to errors that vanish in the limit of large N. As a result, we rigorously confirm the validity of Bogoliubov's 1947 theory, predicting the independence of the low energy behavior of dilute Bose gases on the fine details of the interaction. We finally discuss how this universality result also extends to different scaling regimes and dimensionalities.

Based on joint works with G. Basti, C. Boccato, C.Brennecke, C. Caraci, and B.Schlein.