韩国裸舞

Bose-Einstein condensation in dilute, trapped gases at positive temperature

We consider an interacting, dilute Bose gas trapped in a harmonic potential at positive temperature, in a combination of a thermodynamic and a Gross-Pitaevskii (GP) limit. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose-Einstein condensation, in the sense that the one-particle density matrix of the interacting Gibbs state is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.

(Joint work with A. Deuchert and J. Yngvason)