Proof of Bose-Einstein Condensation for Dilute Trapped Gases

Elliott H. Lieb and Robert Seiringer
Phys. Rev. Lett. 88, 170409 – Published 16 April 2002
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Abstract

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schrödinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.

  • Received 18 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.170409

©2002 American Physical Society

Authors & Affiliations

Elliott H. Lieb and Robert Seiringer*

  • Department of Physics, Jadwin Hall, Princeton University, P.O. Box 708, Princeton, New Jersey 08544

  • *On leave from Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria.

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Vol. 88, Iss. 17 — 29 April 2002

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