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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 | ||||
| Dates: |
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| 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 |
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