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arXiv · 1205.6388

Universal properties of Fermi gases in arbitrary dimensions

Manuel Valiente·Nikolaj T. Zinner·Klaus Molmer
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Abstract

We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial dimensions, interacting via a Dirac delta potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to arbitrary dimension and we obtain a set of universal relations for the Fermi gas. Three-dimensional scattering under very general conditions of transversal confinement is described by an effectively reduced-dimensional scattering length, which we show depends on the three-dimensional scattering length in a universal way. Our formula for non-integer dimensions interpolates between the known results in integer dimensions 1, 2 and 3. Without any need to solve the associated multichannel scattering problem, we find that confinement-induced resonances occur in all dimensions different from D=2, while reduced-dimensional contacts, related to the tails of the momentum distributions, are connected to the three-dimensional contact by a correction factor of purely geometric origin.

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Manuel Valiente, Nikolaj T. Zinner, Klaus Molmer. 2012-10-22. Universal properties of Fermi gases in arbitrary dimensions. https://doi.org/10.1103/physreva.86.043616

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