M. Fortes

Cooper pairs as resonances

Abstract Using the Bethe–Salpeter (BS) equation, Cooper pairing can be generalized to include contributions from holes as well as particles from the ground state of either an ideal Fermi gas (IFG) or of a BCS many-fermion state. The BCS model interfermion interaction is employed throughout. In contrast to the better-known original Cooper pair (CP) problem for either two particles or two holes, the generalized Cooper equation in the IFG case has no real-energy solutions. Rather, it possesses two complex-conjugate solutions with purely imaginary energies. This implies that the IFG ground state is unstable when an attractive interaction is switched on. However, solving the BS equation for the BCS ground state reveals two types of real solutions: one describing moving (i.e., having nonzero total, or center-of-mass, momenta) CPs as resonances (or bound composite particles with a finite lifetime), and another exhibiting superconducting collective excitations analogous to Anderson–Bogoliubov–Higgs RPA modes. A Bose–Einstein-condensation-based picture of superconductivity is addressed.

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM) and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent linear term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory per se, is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality

Padé approximants and the random close packing of hard spheres and disks

dl~2

Linear to quadratic crossover of Cooper-pair dispersion relation

for quadratic dispersion, but is nonzero for all

Low-dimensional BEC

dg~1

Dimensional crossover of a boson gas in multilayers

for linear dispersion.

Bose-Einstein Condensation in Multilayers

It is shown that the highest order Pade approximants based on the known virial expansion in powers of the density for a classical gas of hard spheres are consistent with the empitical value of the random close packing density where the pressure diverges. (AIP)

Harmonically trapped ideal quantum gases

Abstract Cooper pairing is studied in three dimensions to determine its binding energy for all coupling using a general separable interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A coupling-independent linear term in the CMM dominates the pair excitation energy in weak coupling and/or high fermion density, while the more familiar quadratic term prevails only in the extreme low-density (i.e., vacuum) limit for any nonzero coupling. The linear-to-quadratic crossover of the CP dispersion relation is analyzed numerically, and is expected to play a central role in a model of superconductivity (and superfluidity) simultaneously accommodating a Bardeen–Cooper–Schrieffer condensate as well as a Bose–Einstein condensate of CP bosons.

Hard-sphere fluid-to-solid transition and the virial expansion

The Bose-Einstein condensation (BEC) temperature Tc of Cooper pairs (CPs) created from a general interfermion interaction is determined for a linear, as well as the usually assumed quadratic, energy vs center-of-mass momentum dispersion relation. This explicit Tc is then compared with a widely applied implicit one of Wen & Kan (1988) in d=2+∈ dimensions, for small ∈, for a geometry of an infinite stack of parallel (e.g., copperoxygen) planes as in, say, a cuprate superconductor, and with a new result for linear-dispersion CPs. The implicit formula gives Tc values only slightly lower than those of the explicit formula for typical cuprate parameters.

Superfluidity of a spin-imbalanced Fermi gas in a three-dimensional optical lattice

We obtain the thermodynamic properties for a noninteracting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability P{>=}0 between layers. The BEC critical temperature T{sub c} coincides with the ideal gas BEC critical temperature T{sub 0} when P=0 and rapidly goes to zero as P increases to infinity for any finite interlayer separation. The specific heat C{sub V} as a function of absolute temperature T for finite P and plane separation a exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than that of BEC T{sub c}. This highlights the effects due to particle confinement. We then discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of P. For T T{sub c}, it is exhibited by a broad minimum in C{sub V}(T).