I will discuss a recent result about the excitation spectrum of a dilute Bose gas. We start from the microscopic many-body Hamiltonian H_N of quantum mechanics and derive Bogoliubov’s prediction for the first eigenvalues of H_N in the Gross—Pitaevskii regime for the inhomogeneous case (with an external field). We show that in this limit, the Hamiltonian H_N can be well approximated to the second order by a quadratic Hamiltonian describing a system of non-interacting quasi-particles.
This is joint work with P.T. Nam

https://teams.microsoft.com/l/meetup-join/19%3ae0d8264434a94a2e93fc6ae0fea08c92%40thread.tacv2/1645985098208?context=%7b%22Tid%22%3a%222fa58faf-7eb1-48b9-9964-a92659d1c5b8%22%2c%22Oid%22%3a%22cac978ae-4f05-466e-9520-2df38186dacf%22%7d
https://indico.math.cnrs.fr/event/7325/