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Comparison between microscopic methods for finite-temperature Bose gases

Lookup NU author(s): Dr Stuart Cockburn, Professor Nikolaos ProukakisORCiD


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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.

Publication metadata

Author(s): Cockburn SP, Negretti A, Proukakis NP, Henkel C

Publication type: Article

Publication status: Published

Journal: Physical Review A

Year: 2011

Volume: 83

Issue: 4

Print publication date: 21/04/2011

ISSN (print): 1050-2947

ISSN (electronic): 1094-1622

Publisher: American Physical Society


DOI: 10.1103/PhysRevA.83.043619


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Funder referenceFunder name
European Community
Lundbeck Foundation
Forschungsbonus der Universitat Ulm und der Ulmer Universitatsgesellschaft
236073European Union
He-2849/3Deutsche Forschungsgemeinschaft
SFB/TRR21Deutsche Forschungsgemeinschaft