The excitation spectrum of Bose gases interacting through singular potentials

We consider systems of $N$ bosons in a box with periodic boundary conditions, interacting through a repulsive two-body potential of the form $\kappa V(N^\beta x)$. For all $0 < \beta < 1$, and for sufficiently small coupling constant $\kappa > 0$, we establish the validity of Bogoliubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large $N$.

Joint work with Christian Brennecke, Serena Cenatiempo and Benjamin Schlein.