Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases

Abstract

We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a^2 ρis small and the temperature T satisfies T > 4 πρ/ \ln |\ln(a^2ρ). Here, a is the scattering length of the repulsive interaction potential and ρis the density. To leading order in a^2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when ΔT_c / T_c^0 > 5 \sqrt{a ρ^{1/3}}, where T_c^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.

arXiv comment10 pages, 2 figures

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• Hot Topics in Cold Gases
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• The scattering length at positive temperature
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• Thermodynamical properties of a trapped interacting Bose gas
• Limites de champ moyen bosoniques {à} temp{é}rature positive
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