Exact Relations for a Strongly Interacting Fermi Gas from the Operator Product Expansion
Eric BraatenDepartment of Physics, The Ohio State University, Columbus, Ohio 43210, USA. [email protected]Lucas PlatterDepartment of Physics, The Ohio State University, Columbus, Ohio 43210, USA
2008en
ABI
Abstract
The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k4 at large momentum k, as pointed out by 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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