Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Ground-State Entanglement of the BCS Model

The concept of local concurrence is used to quantify the entanglement between a single qubit and the remainder of a multiqubit system. For the ground state of the BCS model in the thermodynamic limit the set of local concurrences completely describes the entanglement. As a measure for the entanglement of the full system we investigate the average local concurrence (ALC). We find that the ALC satisfies a simple relation with the order parameter. We then show that for finite systems with a fixed particle number, a relation between the ALC and the condensation energy exposes a threshold coupling. Below the threshold, entanglement measures besides the ALC are significant.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

A two band model for superconductivity: probing interband pair formation

We propose a two band model for superconductivity. It turns out that the simplest nontrivial case considers solely interband scattering, and both bands can be modeled as symmetric (around the Fermi level) and flat, thus each band is completely characterized by its half-band width Wn (n=1,2). A useful dimensionless parameter is d, proportional to W2 - W1. The case delta = 0 retrieves the conventional BCS model. We probe the specific heat, the ratio gap over critical temperature, the thermodynamic critical field and tunneling conductance as functions of d and temperature (from zero to Tc). We compare our results with experimental results for MgB2 and good quantitative agreement is obtained, indicating the relevance of interband coupling. Work in progress also considers the inclusion of band hybridization and general interband as well as intra-band scattering mechanisms.

The BCS-Bose crossover theory

We contrast four distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and non-condensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h- or 2e-CPs it can do neither. In particular, only half the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures T-c from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the T(c)s of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy). (c) 2007 Published by Elsevier B.V.

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length ξ and a large critical temperature, T c, appropriate for some high-T c materials. The BCS gap, T c, ξ and specific heat C s(T c) as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below T c in p and d waves.

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.

Integrable coupling in a model for Josephson tunneling between non-identical BCS systems

We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of this generalized model is obtained through the Bethe ansatz.

Use of amino acids as counterions improves the solubility of the BCS II model drug, indomethacin

The number of new chemical entities (NCE) is increasing every day after the introduction of combinatorial chemistry and high throughput screening to the drug discovery cycle. One third of these new compounds have aqueous solubility less than 20µg/mL [1]. Therefore, a great deal of interest has been forwarded to the salt formation technique to overcome solubility limitations. This study aims to improve the drug solubility of a Biopharmaceutical Classification System class II (BCS II) model drug (Indomethacin; IND) using basic amino acids (L-arginine, L-lysine and L-histidine) as counterions. Three new salts were prepared using freeze drying method and characterised by FT-IR spectroscopy, proton nuclear magnetic resonance ((1)HNMR), Differential Scanning Calorimetry (DSC) and Thermogravimetric analysis (TGA). The effect of pH on IND solubility was also investigated using pH-solubility profile. Both arginine and lysine formed novel salts with IND, while histidine failed to dissociate the free acid and in turn no salt was formed. Arginine and lysine increased IND solubility by 10,000 and 2296 fold, respectively. An increase in dissolution rate was also observed for the novel salts. Since these new salts have improved IND solubility to that similar to BCS class I drugs, IND salts could be considered for possible waivers of bioequivalence.

Properties of Anisotropic Superconductors in SR Model

The present thesis deals with the theoretical investigations on the effect of anisotropy on various properties of magnetically doped superconductors described by fihiba — Rusinov model.Chapter 1 is introductory. It contains a brief account of the current status of theory of superconductivity. In’ chapter 2 we give the formulation of the problem. Chapter 2.1 gives the BCS theory. The effect of magnetic impurities in superconductors as described by A8 theory is given in chapter 2.2A and that described by SR model is discussed in chapter 2.28. Chapter 2.2c deals with Kondo effect. In chapter 2.3 the anisotropy problem is reviewed. Our calculations, results and discussions are given in chapter 3. Chapter 3.1 deals with Josephson tunnel effect. In chapter 3.2 the thermodynamic critical field H62 is described. Chtpter 3.3 deals with the density of states. The ultrasonic attenuation coefficient and ufitlear spin relaxation are given in chapter 3.4 and 3.5 respectively. In chapter 3.6 we give the upper critical field calculations and chapter 3.7 deals with the response function. The Kondo effect is given in chapter 3.8. In chapter 4 we give the sumary of our results

Gap solitons in a model of a superfluid fermion gas in optical lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear Schrodinger equation for a superfluid Fermi gas in the BCS-BEC crossover

We introduce a quasianalytic nonlinear Schrodinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where k(F)parallel to a parallel to << 1 with a the s-wave scattering length and k(F) the Fermi momentum, through the unitarity limit k(F)a ->+/-infinity to the Bose-Einstein condensation (BEC) regime where k(F)a > 0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.