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DESCRIPTION:Elliott Lieb\, Princeton University\n\nThe peculiar quantum-mec
hanical properties of the ground states of Bose\ngases that were predicted
in the early days of quantum-mechanics have been\nverified experimentally
relatively recently. The mathematical derivation\nof these properties fr
om Schroedinger's equation have also been difficult\,\nbut progress has be
en made in the last few years (with R. Seiringer\,\nJ-P. Solovej and J. Yn
gvason) and this will be reviewed. For the low\ndensity gas with finite ra
nge interactions these properties include\nthe leading order term in the g
round state energy\, the validity of the\nGross-Pitaevskii description in
traps\, Bose-Einstein condensation and\nsuperfluidity in traps\, and the t
ransition from 3-dimensional behavior\nto 1-dimensional behavior as the cr
oss-section of the trap decreases. The\nlatter is a highly quantum-mechani
cal phenomenon.\n\n\nFor the charged Bose gas at high density\, the leadin
g term in the energy\nfound by Foldy in 1961 for the one-component gas and
Dyson's conjecture\nof the N^{7/5} law for the two-component gas has also
been verified. These\nresults help justify Bogolubov's 1947 theory of pai
ring in Bose gases.
DTSTART:20040423T200000Z
LOCATION:Physics Building\, Room 204
SUMMARY:The Dilute\, Cold Bose Gas: A truly quantum-mechanical many-body pr
oblem
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