Proof of Bose-Einstein Condensation for Interacting Gases

Elliou H. Lieb, Robert Seiringer

Markus Holzmann, P. Grüter, Franck Laloë

Élliott H. Lieb, Robert Seiringer

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.

Keith R. Burnett

J. Lauwers, André F. Verbeure, Valentin Anatol'evich Zagrebnov

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose–Einstein condensation for such interacting systems.

Vitaly V. Kocharovsky, Vl. V. Kocharovsky