Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance

Abstract

A set of universal relations between various properties of any few-body or many-body system consisting of fermions with two spin states and a large but finite scattering length have been derived by Shina Tan. We derive generalizations of the Tan relations for a two-channel model for fermions near a Feshbach resonance that includes a molecular state whose detuning energy controls the scattering length. We use quantum field theory methods, including renormalization and the operator product expansion, to derive these relations. They reduce to the Tan relations as the scattering length is made increasingly large.

25 pages, 8 figures

References in corpus (7)

• Theory of ultracold Fermi gases
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Three-boson problem near a narrow Feshbach resonance
• Scattering Models for Ultracold Atoms
• Virial theorems for trapped cold atoms

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