The excitation spectrum of Bose gases interacting through singular potentials

We consider systems of N bosons in a box of volume 1, interacting through a repulsive two-body potential of the form kN^(3b−1)V(Nbx). For all b in the interval (0,1), and for sufficiently small coupling constant k positive, 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.