Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion

Details Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion

2008-03-07

arxiv.org/abs/0803.1125v1

Phys.Rev.Lett.100:205301,2008

Physics

Condensed Matter

Other Condensed Matter

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.100.205301

The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k^4 at large momentum k, as pointed out by Shina Tan. He used novel methods to derive exact relations between the coefficient of the tail in the momentum distribution and various other properties of the system. We present simple derivations of these relations using the operator product expansion for quantum fields. We identify the coefficient as the integral over space of the expectation value of a local operator that measures the density of pairs.

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