Bogoliubov excitation spectrum of trapped Bose gases in the Gross–Pitaevskii regime

Abstract

We consider an inhomogeneous system of N bosons in R3 confined by an external potential and interacting via a repulsive potential of the form N2V(N(x−y)). We prove that the low-energy excitation spectrum of the system is determined by the eigenvalues of an effective one-particle operator, which agrees with Bogoliubov's approximation.