An interacting many-particle quantum system can be drastically affected by a change in the magnitude of one-particle tunneling across a potential barrier. The results which we will present are part of a long-term effort which aims at addressing such a phenomenon. In spite of the huge literature on Schroedinger operators with potential barriers, the influence of tunneling on many-body systems has been little explored so far. We will show that elementary excitations of an interacting Bose gas trapped by a double-well potential are much larger than the one-body gap. The effective model ruling the excitation spectrum is a suitable two-mode Bose-Hubbard Hamiltonian. This will be framed in the context of Bogoliubov's theory. Joint work with Simone Rademacher (LMU Munich) and Nicolas Rougerie (ENS Lyon).

[Il seminario si svolgerà all'interno delle attività del progetto PRIN 2022CHELC7 "Singular Interactions and Effective Models in Mathematical Physics" finanziato dall’Unione europea – Next Generation EU.]