Mathematical Analysis of Dilute Quantum Gases

This research project deals with the mathematical analysis of the ground state properties of dilute quantum gases. These are of considerable interest for the understanding of recent experiments on Bose-Einstein condensation. Based on a work of Lieb, Seiringer and Yngvason, which gives a proof of the asymptotic exactness of the so- called Gross-Pitaevskii approximation for dilute Bose gases with repulsive interaction, various extensions are considered. These cover the generalization of the work mentioned above to partially attractive interaction among the particles, higher corrections to the leading order, the case of a rotating Bose gas and the proof of Bose condensation in the ground state. Moreover, the fermionic analogue will be investigated, namely the dilute, interacting Fermi gas. These items shall be treated within the next two years in collaboration with Prof. Elliott H. Lieb at Princeton university.