Author(s):

Deuchert, Andreas; Seiringer, Robert; Yngvason, Jakob

Article Title: 
Bose–Einstein condensation in a dilute, trapped gas at positive temperature

Affiliation 
IST Austria 
Abstract: 
We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. 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 following sense: The oneparticle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.

Journal Title:

Communications in Mathematical Physics

ISSN:

14320916

Publisher:

Springer

Date Published:

20180830

Start Page: 
epub ahead of print

Copyright Statement: 
CC BY 4.0

DOI: 
10.1007/s0022001832390

Open access: 
yes (OA journal) 