Algebraic Bethe Ansatz for a discrete-state BCS pairing model

We show in detail how Richardson's exact solution of a discrete-state BCS (DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz solution of the inhomogeneous XXX vertex model with twisted boundary conditions: by implementing the twist using Sklyanin's K-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe Ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the H_i as Hamiltonian, more general exactly solvable models can be constructed. -- To make the paper accessible to readers that are not Bethe Ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.

Detailed analysis of low energy plasma data under the Voyager Uranus data analysis program

Research effort included the PLS data analysis program where modifications to the data fitting procedure and elimination of possible noise and electron contamination were made. The analysis code corrections were used in checking the Neptune data gathered during the Voyager 2 encounter and for analyzing selected plasma spectra from the warm Io torus. A major task accomplished was the summary of Uranus-related research in the U.S. National Report to the International Union of Geodesy and Geophysics for the 1987 - 1990 quadrennium. A limited amount of work was accomplished on assessing the Pedersen conductivity of the ionosphere and comparing it with inferred values from shielding by the Uranian ring current. Under this grant there has been a great deal of effort expended on identifying and classifying plasma waves and oscillations in the magnetosheath and solar wind downstream from Uranus. Large amplitude oscillations in plasma parameters are found in the magnetosheath, with density changes of up to a factor of ten occurring on times scales of minutes. New algorithms developed for analyzing the inbound bow shock crossing of Neptune will probably be applied to a more detailed analysis of the Uranus shock in the near future

Integrable model for interacting electrons in metallic grains

We find an integrable generalization of the BCS model with non-uniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the ``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.Comment: 4 pages, revtex. Revised version to be published in Phys. Rev. Let

Isolated quadriceps training restores whole body exercise capacity in CHF

Patients with Chronic Heart Failure (CHF) are commonly characterized by exercise limitation. The benefit of isolated (i.e., small muscle mass) muscle training and its potential translation to whole body exercise in patients CHF has been recognized, however the mechanisms responsible for this positive outcome remain poorly understood. To study oxygen (O2) transport and metabolism at maximal cycle (whole body) and knee extensor (KE, small muscle mass) exercise in this pathological condition, eight healthy controls and six patients with CHF with reduced ejection fraction commenced 8 weeks of KE training (both legs, separately). Before and after training, they underwent cycle and KE maximal exercise studies. Pre-training cycling and KE exercise peak leg O2 uptake (VO2) were 17% and 15% lower, respectively, in the patients compared to controls. Although KE training did not alter cardiac output at maximal KE or cycle exercise, it increased O2 delivery (by 54%), arterial-venous O2 difference (by 10%), and muscle O2 conductance (by 39%) at maximal KE exercise, yielding an increase in peak single leg VO2 of 53%, which exceeded untrained control subject values. Post-training, during maximal cycling, O2 delivery (40%), arterial-venous O2 difference (15%), and muscle O2 conductance (DMO2) (52%) all increased, yielding a 40% greater peak leg VO2, matching that of the controls. Small muscle mass exercise training-induced improvements in both peripheral convective and diffusive O2 transport and subsequent O2 utilization were the main mechanisms responsible for the increased whole body exercise capacity in patients with CHF. Such clear improvements in these factors and exercise capacity support the efficacy of small muscle mass training as a powerful approach to promote a metabolic reserve and maintain physical function in the face of continuing central limitations associated with CHF

Thermodynamic properties of a small superconducting grain

The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered. The crossover between the ultrasmall regime, in which the level spacing, $d$, is larger than the bulk superconducting gap, $\Delta$, and the small regime, where $\Delta \gtrsim d$, is investigated analytically and numerically. The condensation energy, spin magnetization and tunneling peak spectrum are calculated analytically in the ultrasmall regime, using an approximation controlled by $1/\ln N$ as small parameter, where $N$ is the number of interacting electron pairs. The condensation energy in this regime is perturbative in the coupling constant $\lambda$, and is proportional to $d N \lambda^2 = \lambda^2 \omega_D$. We find that also in a large regime with $\Delta>d$, in which pairing correlations are already rather well developed, the perturbative part of the condensation energy is larger than the singular, BCS, part. The condition for the condensation energy to be well approximated by the BCS result is found to be roughly $\Delta > \sqrt{d \omega_D}$. We show how the condensation energy can, in principle, be extracted from a measurement of the spin magnetization curve, and find a re-entrant susceptibility at zero temperature as a function of magnetic field, which can serve as a sensitive probe for the existence of superconducting correlations in ultrasmall grains. Numerical results are presented which suggest that in the large $N$ limit the 1/N correction to the BCS result for the condensation energy is larger than $\Delta$.Comment: 17 pages, 7 figures, Submitted to Phys. Rev.

Re-entrant spin susceptibility of a superconducting grain

We study the spin susceptibility chi of a small, isolated superconducting grain. Due to the interplay between parity effects and pairing correlations, the dependence of chi on temperature T is qualitatively different from the standard BCS result valid in the bulk limit. If the number of electrons on the grain is odd, chi shows a re-entrant behavior as a function of temperature. This behavior persists even in the case of ultrasmall grains where the mean level spacing is much larger than the BCS gap. If the number of electrons is even, chi(T) is exponentially small at low temperatures.Comment: 9 pages, 3 figures. To be published in PR