Time: Monday, 4pm.
Abstract: One of the most beautiful chapters of theoretical physics is the analysis of excitation spectrum of the Bose gas due to Bogoliubov. Clearly, this analysis is nonrigorous. However it has been qualitatively confirmed by experiments and underlies our understanding of one of the most remarkable physical phenomena -- the superfluidity.
I will describe a rigorous result saying that, appropriately interpreted, Bogoliubov's picture is correct in a certain limit that involves a large number of particles and large volume. According to this result, in this limit the joint spectrum of the many-body Schrödinger Hamiltonian and the momentum has a special shape predicted by Bogoliubov.
I do not expect that everybody in the audience is familiar with the physics jargon. The results and tools that I am going to describe can be understood and appreciated purely in the context of spectral theory of operators on Hilbert spaces.