APDE seminar@UPV/EHU: A novel method for the derivation of a universal expansion for the free energy of a Bose gas

Abstract

The Lee-Huang-Yang formula provides a universal expression for the first two terms in the dilute regime expansion of the energy density of a Bose gas in the thermodynamic limit. In the model considered, the particles interact through a pairwise, spherically symmetric, repulsive potential. This universality lies in its dependence solely on the scattering length of the interaction potential, irrespective of the potential’s specific shape. Introducing a new method that combines the renormalization of the potential with a Neumann localization, we establish a lower bound for the free energy density at low temperatures for a broad class of singular potentials, including the case of hardcore interactions. The derived expression incorporates the Lee-Huang-Yang terms along with an additional thermal contribution arising from the excitation spectrum.

From a joint work with S. Fournais, T. Girardot, L. Junge, L. Morin, and A. Triay.