The excitation spectrum of Bose gases interacting through singular potentials

Abstract

We consider systems of $N$ bosons in a box of volume one, interacting through a repulsive two-body potential of the form $\kappa N^{3\beta -1}V(N^{\beta }x)$. For all $0<\beta <1$, and for sufficiently small coupling constant $\kappa >0$, we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large $N$.