Toshiaki Iida and Miki Wadati J. Stat. Mech. (2007) P06011 doi:10.1088/1742-5468/2007/06/P06011
Exact analysis of a δ-function spin-1/2 attractive Fermi gas with arbitrary polarization
Toshiaki Iida and Miki Wadati
Show affiliationsThe ground state of a one-dimensional δ-function attractive spin-1/2 fermions is studied by the nested Bethe ansatz method. Explicitly, the Gaudin integral equation for the system is solved in the form of power series with arbitrary spin polarization. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. The physical quantities, such as the ground state energy and the chemical potentials, are expressed in terms of the dimensionless coupling constant 
and the polarization 
, where c is the coupling constant and 
are the number densities of the spin-up (down) particles. While in the limiting case P = 1, the system consists of spinless free fermions, the other limit P = 0 describes the BCS–BEC crossover in one dimension. As a function of P, the evolution is continuous and smooth.
- Keywords
- PACS
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05.30.Fk Fermion systems and electron gas
02.30.Mv Approximations and expansions
02.30.Lt Sequences, series, and summability
03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow
- MSC
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82B30 Statistical thermodynamics (See also 80-XX)
82B23 Exactly solvable models; Bethe ansatz
81Q40 Bethe-Salpeter and other integral equations
82B10 Quantum equilibrium statistical mechanics (general)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (See also 30E15)
- Subjects
- Dates
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Issue 06 (June 2007)
Received 4 May 2007, accepted for publication 22 May 2007
Published 14 June 2007
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Exact analysis of a δ-function spin-1/2 attractive Fermi gas with arbitrary polarization
Toshiaki Iida and Miki Wadati J. Stat. Mech. (2007) P06011
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