Tan's distributions and Fermi-Huang pseudopotential in momentum space

Abstract

The long-standing question of finding the momentum representation for the s-wave zero-range interaction in three spatial dimensions is here solved. This is done by expressing a certain distribution, introduced in a formal way by S. Tan [Ann. Phys. 323, 2952 (2008)], explicitly. The resulting form of the Fourier-transformed pseudopotential remains very simple. Operator forms for the so-called Tan's selectors which, together with Fermi-Huang pseudopotential, largely simplify the derivation of Tan's universal relations for the Fermi gas, are here derived and are also very simple. A momentum cut-off version of the pseudopotential is also provided, and with this no apparent contradiction with the notion of integrals in Tan's methods is left. The equivalence, even at the intermediate step level, between the pseudopotential approach and momentum-space renormalization of the bare Dirac delta interaction is then shown by using the explicit form of the cut-off pseudopotential.

5 pages, no figures

References in corpus (6)

• Many-Body Physics with Ultracold Gases
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Verification of universal relations in a strongly interacting Fermi gas
• Epsilon expansion for a Fermi gas at infinite scattering length
• Crossover in the Efimov spectrum

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• Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits
• Universal relations for a spin-polarized Fermi gas in two dimensions
• Spectral flow of trimer states of two heavy impurities and one light condensed boson
• Single-branch theory of ultracold Fermi gases with artificial Rashba spin-orbit coupling
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• From few to many body degrees of freedom