The scattering length at positive temperature

Details The scattering length at positive temperature The scattering length at positive temperature

2011-11-07

arxiv.org/abs/1111.1683v1

Physics

Mathematical Physics

LaTeX, 6 pages

Scientific paper

A positive temperature analogue of the scattering length of a potential $V$ can be defined via integrating the difference of the heat kernels of $-\Delta$ and $-\Delta + \frac 12 V$, with $\Delta$ 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 \cite{SU}. In \cite{SU} 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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