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Fermi-Bose mapping and N-particle ground state of spin-polarized fermions in tight atom waveguides

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arxiv cond-mat/0309396 v1 pith:OY2VJ3E3 submitted 2003-09-17 cond-mat.soft

M. D. Girardeau , M. Olshanii This is my paper · ORCID
classification cond-mat.soft
keywords fermionsspin-polarizedfermionicinteractionstightwaveguidebosebosons
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A K-matrix for waveguide confined spin-polarized fermionic atoms recently computed by Granger and Blume is identified, in the low-energy domain, with a contact condition for one-dimensional (1D) spinless fermions. Difficulties in consistently formulating the contact conditions in terms of interaction potentials are discussed and a rigorous alternative variational reformulation is constructed. A duality between 1D fermions and bosons with zero-range interactions suggested by Cheon and Shigehara is shown to hold for the effective 1D dynamics of a spin-polarized Fermi gas with 3D p-wave interactions and that of a Bose gas with 3D s-wave interactions in a tight waveguide. This generalizes the mapping from impenetrable bosons (TG gas) to free fermions and is used to derive the equation of state of an ultracold spin-polarized fermionic vapor in a tight waveguide. Near a 1D confinement-induced resonance one has a "fermionic TG gas" which maps to an ideal Bose gas.

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Cited by 2 Pith papers

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  1. Two identical 1D anyons with zero-range interactions: Exchange statistics, scattering theory, and anyon-anyon mapping

    quant-ph 2025-05 conditional novelty 6.0 of 10

    Develops a scattering framework for two 1D anyons with zero-range interactions, derives their momentum distribution tails to order k^{-4}, and confirms a bosonic-anyon to fermionic-anyon mapping.

  2. Universal momentum tail of identical one-dimensional anyons with two-body interactions

    cond-mat.quant-gas 2025-05 conditional novelty 6.0 of 10

    One-dimensional bosonic and fermionic anyons with zero-range interactions have distinct universal momentum tails, with k^-2 and k^-3 prefactors set by the statistical parameter, the scattering length, and the two- and...

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