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Rigorous results on the interacting Bose gas

Mathematical Physics & Probability

Speaker: Robert Seiringer, Princeton University
Location: 693 Kerr
Start time: Tue, Apr 15 2003, 3:10PM

We present a summary of recent results on the interacting Bose gas, that were obtained in joint work with Elliott Lieb and Jakob Yngvason. The ground state of a dilute Bose gas in a trap, as considered in recent experiments, is usually described by means of the Gross-Pitaevskii equation, a non-linear one-particle Schroedinger equation. We clarify its status as an approximation to the quantum mechanical many-body ground state problem. In addition, we prove the existence of Bose-Einstein condensation and Superfluidity in the dilute limit. If time permits, we also discuss the generalization of our results to rotating systems, and investigate the effect of a breaking of the rotational symmetry.