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

Beau, Mathieu and Savoie, Baptiste (2013) The ideal Bose gas in open harmonic trap systems and its condensation revisited. (Preprint)

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Quantum statistical mechanics, cold atomic gases, Bose-Einstein condensation (BEC), inhomogeneous systems, harmonic potential, thermodynamic limit, weak-harmonic limit, Penrose- Onsager criterion
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:49
Last Modified: 12 Jul 2018 13:40
URI: http://dair.dias.ie/id/eprint/537

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