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Bose-Einstein Condensation of Dilute Gases in Traps

Elliott H. Lieb·Robert Seiringer
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Abstract

The ground state of a gas of Bosons confined in an external trap potential and interacting via repulsive two-body forces has recently been shown to exhibit complete Bose-Einstein condensation in the dilute limit, yielding for the first time a rigorous proof of this phenomenon in a physically realistic setting. We give here an account of this work about the Gross-Pitaevskii limit where the particle number $N$ goes to infinity with $Na$ fixed, where $a$ is the scattering length of the interparticle interaction, measured in units of the trap size.

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Elliott H. Lieb, Robert Seiringer. 2002-10-13. Bose-Einstein Condensation of Dilute Gases in Traps. https://arxiv.org/abs/math-ph/0210028

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