Abstract
A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of −Δ and \({-\Delta + \frac{1}{2}V}\), with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range.
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References
Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions. Dover, Kent (1964)
Lieb, E.H., Seiringer, R., Solovej, J.P., Yngvason, J.: The Mathematics of the Bose Gas and its Condensation, Oberwolfach Seminars, vol. 34. Birkhäuser, Basel (2005). http://arxiv.org/abs/cond-mat/0610117
Lieb E.H., Yngvason J.: The ground state energy of a dilute two-dimensional Bose gas. J. Stat. Phys. 103, 509 (2001)
Seiringer R., Ueltschi D.: Rigorous upper bound on the critical temperature of dilute Bose gases. Phys. Rev. B 80, 014502 (2009)
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Landon, B., Seiringer, R. The Scattering Length at Positive Temperature. Lett Math Phys 100, 237–243 (2012). https://doi.org/10.1007/s11005-012-0566-5
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DOI: https://doi.org/10.1007/s11005-012-0566-5