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Comparison between microscopic methods for finite-temperature Bose gases
Lookup NU author(s)
Dr Stuart Cockburn
Professor Nikolaos Proukakis
Author(s)
Cockburn SP, Negretti A, Proukakis NP, Henkel C
Publication type
Article
Journal
Physical Review A
Year
2011
Volume
83
Issue
4
Pages
ISSN (print)
1050-2947
ISSN (electronic)
1094-1622
Full text for this publication is not currently held within this repository. Alternative links are provided below where available.
We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (ncB) approach and a stochastic Gross-Pitaevskii equation (sGPe) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the ncB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (ncB: canonical, sGPe: grand-canonical), they yield the correct condensate statistics in a large BEC (strong enough particle interactions). For smaller systems, the sGPe results are prone to anomalously large number fluctuations, well-known for the grand-canonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the Penrose-Onsager condensate from first- and second-order correlation functions that is computationally convenient. This also clarifies the link between condensate and quasi-condensate in the Popov theory of low-dimensional systems.
Publisher
American Physical Society
URL
http://dx.doi.org/10.1103/PhysRevA.83.043619
DOI
10.1103/PhysRevA.83.043619
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