Friday, April 23, 2004
4:00 PM
Physics Building, Room 204
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"The Dilute, Cold Bose Gas: A truly quantum-mechanical many-body problem"

Elliott Lieb , Princeton University
[Host: E. Kolomeisky]
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 have 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 description in traps, Bose-Einstein condensation and superfluidity in traps, 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. For the charged Bose gas at high density, the leading term in the energy found by Foldy in 1961 for the one-component gas and Dyson's conjecture of the N^{7/5} law for the two-component gas has also been verified. These results help justify Bogolubov's 1947 theory of pairing in Bose gases.

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