Rigorous upper bound on the critical temperature of dilute Bose gases

R. Seiringer, D. Ueltschi, Physical Review B - Condensed Matter and Materials Physics 80 (2009).


Journal Article | Published
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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

Cite this

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, 80(1). 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 80, no. 1 (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, 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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