The dynamical similarities between the three-dimensional (3D) electron fluid ``jellium'' model and the exactly soluble 1D fermion fluid with attractive \ensuremath{\delta}-function pairwise potentials motivates solving the Cooper-pair problem in this model for all couplings and/or densities. This is accomplished exactly in graphical form. For weak coupling, the essential singularity characteristic of standard 3D low-temperature superconductivity reemerges, and for infinite coupling, BCS theory reproduces the exact ground-state system energy.The dynamical similarities between the three-dimensional (3D) electron fluid ``jellium'' model and the exactly soluble 1D fermion fluid with attractive \ensuremath{\delta}-function pairwise potentials motivates solving the Cooper-pair problem in this model for all couplings and/or densities. This is accomplished exactly in graphical form. For weak coupling, the essential singularity characteristic of standard 3D low-temperature superconductivity reemerges, and for infinite coupling, BCS theory reproduces the exact ground-state system energy.

Physical Review AOct 1, 199117 citations

Pairing in Fermion Systems

S. Mazumdar

Physical Review LettersNov 30, 19872 citations

An Exactly Solvable Many-Fermion Model

Nouredine Zettili

APSApr 1, 20010 citations

Coherent correlated pair method for N -fermion systems

James P. Vary, Angelo Plastino

We develop a method for treating the $N$ -fermion problem as a system of correlated pairs of particles. Coherent pair states are introduced and a variational as well as a secular method are discussed for providing upper bounds to the exact ground state and approximations to the low lying spectra. Specific applications to two soluble models are presented. For these models the coherent correlated pair method is superior to the Bardeen-Cooper-Schrieffer approximation and to the Hartree-Fock approximation and in fact yields the exact solutions for all particle numbers and sufficiently large coupling constants.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bound to ground state energy; applications to soluble $N$ -fermion models.We develop a method for treating the $N$-fermion problem as a system of correlated pairs of particles. Coherent pair states are introduced and a variational as well as a secular method are discussed for providing upper bounds to the exact ground state and approximations to the low lying spectra. Specific applications to two soluble models are presented. For these models the coherent correlated pair method is superior to the Bardeen-Cooper-Schrieffer approximation and to the Hartree-Fock approximation and in fact yields the exact solutions for all particle numbers and sufficiently large coupling constants.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bound to ground state energy; applications to soluble $N$-fermion models.

Physical Review CDec 1, 19837 citations

We develop a method for treating the

N

-fermion problem as a system of correlated pairs of particles. Coherent pair states are introduced and a variational as well as a secular method are discussed for providing upper bounds to the exact ground state and approximations to the low lying spectra. Specific applications to two soluble models are presented. For these models the coherent correlated pair method is superior to the Bardeen-Cooper-Schrieffer approximation and to the Hartree-Fock approximation and in fact yields the exact solutions for all particle numbers and sufficiently large coupling constants.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bound to ground state energy; applications to soluble

N

-fermion models.