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Title: Threshold singularities in a Fermi gas with attractive potential in one dimension

We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ-function potential using the Bethe Ansatz solution. In zero magnetic field the atoms form bound states of N=2S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c=1. The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe Ansatz solution we obtain expressions for the critical exponents for the single-particle (hole) Green’s function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.
Authors:
ORCiD logo [1] ;  [2]
  1. Florida State University, Tallahassee, FL (United States)
  2. Ukrainian National Academy of Sciences, Kharkov (Ukraine); Max-Planck-Institut für Physik komplexer Systeme, Dresden (Germany)
Publication Date:
OSTI Identifier:
1228398
Grant/Contract Number:
FG02-98ER45707; 4-15-13
Type:
Published Article
Journal Name:
Nuclear Physics. B
Additional Journal Information:
Journal Volume: 892; Journal Issue: C; Journal ID: ISSN 0550-3213
Publisher:
Elsevier
Research Org:
Florida State Univ., Tallahassee, FL (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS