In their celebrated paper of 1957, Lee, Huang and Yang computed the excitation spectrum of dilute Bose gases. I will talk about a series of recent works where we justified this formula by proving an expansion of the free energy for low temperature hence capturing the effects of the quantum fluctuations.
This is based on joint works with S. Fournais, T. Girardot, F. Haberberger, C. Hainzl, L. Junge, L. Morin, P.T. Nam, M. Olivieri, B. Schlein, R. Seiringer