Comparison between microscopic methods for finite-temperature Bose gases

Journal Article · Fri Apr 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.043619· OSTI ID:21544680

Cockburn, S P; Proukakis, N P ^[1]; Negretti, A ^[2]; Henkel, C ^[3]

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1. School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU (United Kingdom)
2. Lundbeck Foundation Theoretical Center for Quantum System Research, Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C (Denmark)
3. Institut fuer Physik und Astronomie, Universitaet Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam (Germany)

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 Bose-Einstein condensate (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 both computationally convenient and of potential use to experimentalists. This also clarifies the link between condensate and quasicondensate in the Popov theory of low-dimensional systems.

• OSTI ID: 21544680
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
BOSE-EINSTEIN GAS
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
CORRELATION FUNCTIONS
DENSITY
EQUATIONS
EVALUATION
FLUCTUATIONS
FUNCTIONS
INTERACTIONS
MATHEMATICS
ONE-DIMENSIONAL CALCULATIONS
PARTICLE INTERACTIONS
PERTURBATION THEORY
PHYSICAL PROPERTIES
SIMULATION
SPECTRA
STATISTICS
STOCHASTIC PROCESSES
TEMPERATURE RANGE
TEMPERATURE RANGE 0065-0273 K
TRAPPING
VARIATIONS