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 |
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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: | 17 Dec 2022 14:41 |
URI: | https://dair.dias.ie/id/eprint/537 |
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