M. de Llano

Multiple phases in a new statistical boson–fermion model of superconductivity

We apply a new statistical complete boson–fermion model (CBFM) to describe superconductivity with arbitrary departure from the perfect two-electron (2e) and two-hole (2h) Cooper pair (CP) symmetry to which BCS theory is restricted. The model is complete in that it accounts for both 2h and 2e CPs. In special cases the CBFM reduces to all the main statistical continuum models of superconductivity. From it four stable thermodynamic phases emerge around the BCS state, a normal and three stable Bose–Einstein condensed phases of which one is mixed (with both CP types) and two pure. Critical temperatures Tc for the new pure phases rise as one departs from the mixed BCS state, and can result in substantially higher Tcs than with BCS theory for moderate departures from perfect 2e/2h CP symmetry.

Bose-Einstein condensation in the relativistic ideal Bose gas

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is lower with antibosons, thus implying that omitting antibosons always leads to the computation of a metastable state.

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

Studies on nuclear structure in the 2s-1d shell: (II). Application to nuclei with A = 18 and A = 20

dl~2

Bose-Einstein condensation with a BCS model interaction

for quadratic dispersion, but is nonzero for all

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

dg~1

STUDIES ON NUCLEAR STRUCTURE IN THE 2s-1d SHELL. I. METHODS OF GROUP THEORY AND A MODEL INTERACTION

for linear dispersion.

The Cooper pair dispersion relation

Abstract In a previous paper we introduced a model interaction containing quadrupole-quadrupole, orbital pairing and spin-orbit terms. In this paper we obtain the explicit matrices of the model interaction for systems of two and four particles in the 2s-1d shell. We compare the eigenvalues of these matrices with the energy levels of F 18 , O 18 , Ne 20 , O 20 and F 20 obtaining the values of the parameters in the model interaction that give the best fit. Furthermore, we give the explicit expression for states of two and four particles in the 2s-1d shell in the SU 3 classification and obtain the eigenstates of the model interaction in terms of these states.

Two singular potentials: The space‐splitting effect

Abstract A simple model of a boson-fermion mixture of unpaired fermions plus linear-dispersion-relation Cooper pairs that includes pair-breaking effects leads to Bose-Einstein condensation for dimensions greater than unity, at critical temperatures substantially greater than those of the BCS theory of superconductivity, for the same BCS model interaction between the fermions.