The ideal Bose gas in open harmonic trap systems and its condensation revisited.

Baptiste Savoie (1) , Mathieu Beau (2)

1 Aarhus University [Aarhus]
2 STP-DIAS - School of Theoretical Physics [Dublin]

We rigorously revisit a textbook model used to figure out the Bose-Einstein condensation (BEC) phenomenon created by dilute cold alkali atoms gases in a magnetic-optical trap. It consists of a d-dimensional (d=1,2,3) ideal non-relativistic spin-0 Bose gas confined in a box and trapped in an isotropic harmonic potential. Throughout we review and clarify a series of methods involved in the derivation of the thermodynamics in the grand-canonical situation. To make the derivation consistent with the usual rules of the statistical mechanics, we assign through our open-trap limit approach the role of canonical parameter to a rescaled number of particles (instead of an effective density involving the pulsation of the trap). Within this approach, we formulate an Einstein-like and Penrose-Onsager-like criterion of BEC and show their equivalence. Afterwards, we focus on the spatial localization of the condensate/thermal gas. When dealing with the reduced density matrix, our method is similar to the loop path approach.

Mots clés: Quantum statistical mechanics; cold atomic gases; Bose-Einstein condensation (BEC); Penrose-Onsager criterion; inhomogeneous systems; harmonic potential; thermodynamic limit; weak-harmonic limit; Penrose-Onsager criterion.

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Gaz Quantiques [cond-mat.quant-gas]

Baptiste Savoie, Mathieu Beau. The ideal Bose gas in open harmonic trap systems and its condensation revisited.. 2013. ⟨hal-00834558⟩