On Unconventional Electron Pairing In a Periodic Potential

On the assumption that two electrons with the same group velocity effectively attract each other a simple model Hamiltonian is proposed to question the existence of unconventional electron pairs formed by electrons in a strong periodic potential.Comment: 8 page

Analytic Density of States in the Abrikosov-Gorkov Theory

Since the early 1960s, Abrikosov-Gorkov theory has been used to describe superconductors with paramagnetic impurities. Interestingly, the density of states resulting from the theoretical framework has to date only been known approximately, as a numeric solution of a complex polynomial. Here we introduce an exact analytic solution for the density of states of a superconductor with paramagnetic impurities. The solution is valid in the whole regime of Abrikosov-Gorkov theory; both where there is an energy gap and gapless. While of fundamental interest, we argue that this solution also has computational benefits in the evaluation of integrals for tunneling conductances and allows for an analytic description of materials with densities of states that are modeled from the basic Abrikosov-Gorkov density of states.Comment: 5 pages, 1 figur

Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 + y^2, multiplied by an analytic function P(z) of the single complex variable z= x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur

Excitation spectrum of Bilayer ν=2\nu=2 Quantum Hall Systems

Excitation spectra in bilayer quantum Hall systems at total Landau-level filling $\nu=2$ are studied by the Hartree-Fock-Bogoliubov approximation. The systems have the spin degrees of freedom in addition to the layer degrees of freedom described in terms of pseudospin. On the excitation spectra from spin-unpolarized and pseudospin-polarized ground state, this approximation fully preserves the spin rotational symmetry and thus can give not only spin-triplet but also spin-singlet excitations systematically. It is also found that the ground-state properties are well described by this approximation.Comment: 5 pages, 3 figures; conference: EP2DS-1

A Relativistic Separable Potential to Describe Pairing in Nuclear Matter

Using the Dirac-Hartree-Fock-Bogoliubov approximation to study nuclear pairing, we have found the short-range correlations of the Dirac $^1$S$_0$ pairing fields to be essentially identical to those of the two-nucleon virtual state at all values of the baryon density. We make use of this fact to develop a relativistic separable potential that correctly describes the pairing fields.Comment: 17 pages, 4 eps-figure

Symmetry-Projected Hartree-Fock-Bogoliubov Equations

Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using the variational ansatz for the generalized one-body density-matrix in the Valatin form. It is shown that the projected-energy functional can be completely expressed in terms of the HFB density-matrix and the pairing-tensor. The variation of this projected-energy is shown to result in HFB equations with modified expressions for the pairing-potential and the Hartree-Fock field. The expressions for these quantities are explicitly derived for the case of particle number-projection. The numerical applicability of this projection method is studied in an exactly soluble model of a deformed single-j shell.Comment: 24 pages, 1 figur

Bogoliubov Quasiparticle Excitations in the Two-Dimensional t-J Model

Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional $t$$-$$J$ model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in $d_{x^2-y^2}$-wave channel and the energy gap has a size $\Delta_d$$\simeq$$0.15J$$-0.27J$ between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectrum is demonstrated.Comment: 6 pages, RevTe

The Coherence Field in the Field Perturbation Theory of Superconductivity

We re-examine the Nambu-Gorkov perturbation theory of superconductivity on the basis of the Bogoliubov-Valatin quasi-particles. We show that two different fields (and two additional analogous fields) may be constructed, and that the Nambu field is only one of them. For the other field- the coherence field- the interaction is given by means of two interaction vertices that are based on the Pauli matrices tau1 and tau3. Consequently, the Hartree integral for the off-diagonal pairing self-energy may be finite, and in some cases large. We interpret the results in terms of conventional superconductivity, and also discuss briefly possible implications to HTSC

Inequivalent representations of commutator or anticommutator rings of field operators and their applications

Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be an explicit example for the demonstration of the important role of inequivalent representations in practical applications. Its analysis from the inequivalent representations' point of view has led to a recognition of a novel type of the superconducting phase transition.Comment: 25 pages, 6 figure

BCS-like Modewise Entanglement of Fermion Gaussian States

We show that with respect to any bipartite division of modes, pure fermion gaussian states display the same type of structure in its entanglement of modes as that of the BCS wave function, namely, that of a tensor product of entangled two-mode squeezed fermion states. We show that this structure applies to a wider class of "isotropic" mixed fermion states, for which we derive necessary and sufficient conditions for mode entanglement.Comment: 10 pages, RevTex