The BCS - BEC Crossover In Arbitrary Dimensions
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Cold atom traps and certain neutron star layers may contain fermions with separation much larger than the range of pair-wise potentials yet much shorter than the scattering length.
Such systems can display {\em universal} characteristics independent of the details of the short range interactions.
In particular, the energy per particle is a fraction $ξ$ of the Fermi energy of the free Fermion system.
Our main result is that for space dimensions D smaller than two and larger than four a specific extension of this problem readily yields $ξ=1$ for all $D \le 2$ whereas $ξ$ is rigorously non-positive (and potentially vanishing) for all $ D \ge 4$. We discuss the D=3 case. A particular unjustified recipe suggests $ξ=1/2$ in D=3.
9 pages, 1 figure
9 pages, 1 figure