Rigorous upper bound on the critical temperature of dilute Bose gases

Seiringer R, Ueltschi D. 2009. Rigorous upper bound on the critical temperature of dilute Bose gases. Physical Review B - Condensed Matter and Materials Physics. 80(1).


Journal Article | Published
Author
Seiringer, RobertIST Austria ; Ueltschi, Daniel
Abstract
We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2 ρ is small and the temperature T satisfies T> 4πρ ln | ln (a2 ρ) |. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2 ρ, 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 a ρ1/3, 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.
Publishing Year
Date Published
2009-06-02
Journal Title
Physical Review B - Condensed Matter and Materials Physics
Volume
80
Issue
1
IST-REx-ID

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Seiringer R, Ueltschi D. Rigorous upper bound on the critical temperature of dilute Bose gases. Physical Review B - Condensed Matter and Materials Physics. 2009;80(1). doi:10.1103/PhysRevB.80.014502
Seiringer, R., & Ueltschi, D. (2009). Rigorous upper bound on the critical temperature of dilute Bose gases. Physical Review B - Condensed Matter and Materials Physics. American Physical Society. https://doi.org/10.1103/PhysRevB.80.014502
Seiringer, Robert, and Daniel Ueltschi. “Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases.” Physical Review B - Condensed Matter and Materials Physics. American Physical Society, 2009. https://doi.org/10.1103/PhysRevB.80.014502.
R. Seiringer and D. Ueltschi, “Rigorous upper bound on the critical temperature of dilute Bose gases,” Physical Review B - Condensed Matter and Materials Physics, vol. 80, no. 1. American Physical Society, 2009.
Seiringer R, Ueltschi D. 2009. Rigorous upper bound on the critical temperature of dilute Bose gases. Physical Review B - Condensed Matter and Materials Physics. 80(1).
Seiringer, Robert, and Daniel Ueltschi. “Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases.” Physical Review B - Condensed Matter and Materials Physics, vol. 80, no. 1, American Physical Society, 2009, doi:10.1103/PhysRevB.80.014502.
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