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 .