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Rigorous upper bound on the critical temperature of dilute Bose gases

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Seiringer, Robert and Ueltschi, Daniel. (2009) Rigorous upper bound on the critical temperature of dilute Bose gases. Physical Review B (Condensed Matter and Materials Physics), Vol.80 (No.1). 014502. ISSN 1098-0121

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Official URL: http://dx.doi.org/10.1103/PhysRevB.80.014502

Abstract

We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2ρ is small and the temperature T satisfies T>4πρ/ln|ln(a2ρ)|. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T−Tc(0)/Tc(0)>5√aρ1/3, where Tc(0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Phase transformations (Statistical physics), Condensation -- Research, Bosons, Particles (Nuclear physics), Statistical physics -- Research
Journal or Publication Title:	Physical Review B (Condensed Matter and Materials Physics)
Publisher:	American Physical Society
ISSN:	1098-0121
Official Date:	1 July 2009
Volume:	Vol.80
Number:	No.1
Number of Pages:	9
Page Range:	014502
Identification Number:	10.1103/PhysRevB.80.014502
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	National Science Foundation (U.S.) (NSF)
Grant number:	PHY-0652356 (NSF), DMS-0601075 (NSF)
URI:	http://wrap.warwick.ac.uk/id/eprint/2610