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.
Fermi-Bose mapping and N-particle ground state of spin-polarized fermions in tight atom waveguides
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abstract
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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Two identical 1D anyons with zero-range interactions: Exchange statistics, scattering theory, and anyon-anyon mapping
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.