The scattering length at positive temperature

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 $-\Delta$ and $-\Delta +\frac{1}{2}V$, 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.

LaTeX, 6 pages

References in corpus (1)

• Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases

Cited by in corpus (2)

• The free energy of the two-dimensional dilute Bose gas. I. Lower bound
• The free energy of the two-dimensional dilute Bose gas. II. Upper bound