The BCS - BEC Crossover In Arbitrary Dimensions

Details The BCS - BEC Crossover In Arbitrary Dimensions The BCS - BEC Crossover In Arbitrary Dimensions

2004-10-24

arxiv.org/abs/cond-mat/0410597v2

Physics

Condensed Matter

Strongly Correlated Electrons

9 pages, 1 figure

Scientific paper

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 $\xi$ 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 $\xi=1$ for all $D \le 2$ whereas $\xi$ is rigorously non-positive (and potentially vanishing) for all $ D \ge 4$. We discuss the D=3 case. A particular unjustified recipe suggests $\xi=1/2$ in D=3.

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