10th Anniversary Speaker Series 2007

The peculiar quantum-mechanical properties of the ground states of Bose gases that were predicted in the early days of quantum-mechanics have been verified experimentally relatively recently. The mathematical derivation of these properties from Schroedinger's equation has also been difficult, but progress has been made in the last few years (with R. Seiringer, J-P. Solovej and J. Yngvason) and this will be reviewed. For the low density gas with finite range interactions these properties include the leading order term in the ground state energy, the validity of the Gross-Pitaevskii equation in traps (including rapidly rotating traps), Bose-Einstein condensation and superfluidity, and the transition from 3-dimensional behavior to 1-dimensional behavior as the cross-section of the trap decreases. The latter is a highly quantum-mechanical phenomenon.