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Bogoliubov spectrum of interacting Bose gases

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Spectral Theory of Relativistic Operators

We prove that Bogoliubov theory indeed predicts the ground state energy and the excitation spectrum of a very general class of interacting Boses gases. More precisely, we will show that the lower spectrum of the N-body Hamiltonian, in the limit as N tends to infinity, by the spectrum of a quadratic Hamiltonian in Fock space, which is the so-called Bogoliubov Hamiltonian. Such kind of result was already obtained for weakly interacting Bose gases by Seiringer and Grech. Our method is different and it works for a larger class of interactions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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