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 (CP's) 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 d less than or equal to 2 for quadratic dispersion, but is nonzero for all d greater than or equal to 1 for linear dispersion.

Linear to quadratic crossover of Cooper-pair dispersion relation

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. (C) 2001 Elsevier B.V. B,V. All rights reserved.

Pairing symmetries in cuprates: A Gorkov formalism

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Classification of states in S0(8) proton-neutron pairing model

lsoscalar (T = 0) plus isovector (T = 1) pairing Hamiltonian in LS-coupling. which is important for heavy N = Z nuclei, is solvable in terms of a SO(8) Lie algebra for three special values of the mixing parameter that measures the competition between the T = 0 aid T = 1 pairing. The SO(8) algebra is generated, amongst others, by the S = 1, T = 0 and S = 0, T = 1 pair creation and annihilation operators and corresponding to the three values of the mixing parameter, there are three chains of subalgebras: SO(8) superset of SOST (6) superset of SOS(3) circle times SOT(3), SO(8) superset of [SOS(5) superset of SOS(3)] circle times SOT(3) and SO(8) superset of [SOT(5) superset of SOT(3)] circle times SOS(3). Shell model Lie algebras, with only particle number conserving generators, that are complementary to these three chains of subalgebras are identified and they are used in the classification of states for a given number of nucleons. The classification problem is solved explicitly tor states with SO(8) seniority nu = 0, 1, 2, 3 and 4. Using them, hand structures in isospin space are identified for states with nu = 0, 1, 2 and 3. (c) 2005 Elsevier B.V. All rights reserved.

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behaviour in the temperature dependencies of some observables in (s + id)-wave BCS superconductivity in the presence of a weak a wave. We find also a second second-order phase transition. As temperature is lowered-past the usual critical temperature T-c, a less ordered superconducting phase is created in the d wave, which changes to a more ordered phase in a (s + id) wave at T-c1 (

Cooper pair dispersion relation in two dimensions

The Cooper pair binding energy vs. center-of-mass-momentum dispersion relation for Bose-Einstein condensation studies of superconductivity is found in two dimensions for a renormalized attractive delta interaction. It crosses over smoothly from a linear to a quadratic form as coupling varies from weak to strong.

Universal scaling in Bardeen-Cooper-Schrieffer superconductivity in two dimensions in non-s waves

The solutions of a renormalized BCS model are studied in two space dimensions for s, p and d waves for finite-range separable potentials. The gap parameter, the critical temperature T-c, the coherence length xi and the jump in specific heat at T-c as a function of the zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small xi and large T-c, appropriate for high-T-c cuprates. The specific heat, penetration depth and thermal conductivity as functions of temperature show universal scaling for p and d waves.

Q-ANALOG REALIZATION OF NUCLEON PAIRING

A q-deformed analogue of zero-coupled nucleon pair states is constructed and the possibility of accounting for pairing correlations examined. For the single orbit case, the deformed pairs are found to be more strongly bound than the pairs with zero deformation, when a real-valued q parameter is used. It is found that an appropriately scaled deformation parameter reproduces the empirical few nucleon binding energies for nucleons in the 1f7/2 orbit and 1g9/2 orbit. The deformed pair Hamiltonian apparently accounts for many-body correlations, the strength of higher-order force terms being determined by the deformation parameter q. An extension to the multishell case, with deformed zero-coupled pairs distributed over several single particle orbits, has been realized. An analysis of calculated and experimental ground state energies and the energy spectra of three lowermost 0+ states, for even-A Ca isotopes, reveals that the deformation simulates the effective residual interaction to a large extent.

Reproductive compatibility and chromosome pairing in the Drosophila buzzatii complex

Fertility (percentage of fertile crosses) and the degree of synapsis in salivary gland chromosomes in isofemale lines of Drosophila buzzatii, D. serido, D. koepferae and D. seriema were analysed. D. buzzatii was completely sterile in intercrosses with strains from the other species except for D. koepferae. The other species intercrossed to a greater or lesser degree, but also differed between crossing directions. Homologous pairing in salivary gland preparations of strains and hybrids conformed with the data on fertility. The lowest degree of synapsis was present in hybrids between D. koepferae and D. buzzatii, D. seriema and D. koepferae and D. koepferae and D. serido. These species also exhibited the lowest degree of reproductive compatibility. Hybrids between D. seriema and D. serido showed an intermediate degree of synapsis (pairing absent in the proximal and distal chromosome ends), as well as fertility greater than that found in the other interspecific crosses. Results of the fertility of crosses involving strains of a single species, compared with data in the literature, indicated that intraspecific divergence occurred in D. serido and D. koepferae.

Controlling Excitation Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scaling in the BCS to Bose crossover problem in different partial waves

The BCS superconductivity to Bose condensation crossover problem is studied in two dimensions in S, P, and D waves, for a simple anisotropic pairing, with a finite-range separable potential at zero temperature. The gap parameter and the chemical potential as a function of Cooper-pair binding B c exhibit universal scaling. In the BCS limit the results for coherence length ξ and the critical temperature T c are appropriate for highT c cuprate superconductors and also exhibit universal scaling as a function of B c.

Absence of Cooper-type bound states in three- and few-electron systems

It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction.

Meiotic pairing of B chromosomes, multiple sexual system, and Robertsonian fusion in the red brocket deer Mazama americana (Mammalia, Cervidae)

Deer species of the genus Mazama show significant inter and intraspecific chromosomal variation due to the occurrence of rearrangements and B chromosomes. Given that carriers of aneuploidies and structural rearrangements often show anomalous chromosome pairings, we here performed a synaptonemal complex analysis to study chromosome pairing behavior in a red brocket deer (Mazama americana) individual that is heterozygous for a Robertsonian translocation, is a B chromosome carrier, and has a multiple sex chromosome system (XY1Y2). The synaptonemal complex in spermatocytes showed normal chromosome pairings for all chromosomes, including the autosomal and sex trivalents. The electromicrographs showed homology among B chromosomes since they formed bivalents, but they also appeared as univalents, indicating their anomalous behavior and non-Mendelian segregation. Thus, synaptonemal complex analysis is a useful tool to evaluate the role of B chromosomes and rearrangements during meiosis on the intraspecific chromosomal variation that is observed in the majority of Mazama species. © FUNPEC-RP.

Excitonic instabilities and spontaneous time-reversal symmetry breaking on the honeycomb lattice

We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher-order symmetries. Studies of such pairing instabilities have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fermi-liquid excitations. We show that this relationship can be exploited to systematically derive the coupling of the condensate order parameter to the intraband Fermi-liquid particle-hole excitations. Surprisingly, we find that the static susceptibility is negative in the ordered phase when the coupling to the Fermi-liquid collective excitations are included, suggesting that a uniform condensate of virtual excitons, with or without time-reversal breaking, is an unstable phase at T = 0.