Electronic Shell Structure of Nanoscale Superconductors

Motivated by recent experiments on Al nanoparticles, we have studied the effects of fixed electron number and small size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model in two and three dimensions. A negative ``gap'' in particles with an odd number of electrons as observed in the experiments is obtained in our canonical scheme. For particles with an even number of electrons, the energy gap exhibits shell structure as a function of electron density or system size in the weak-coupling regime: the gap is particularly large for ``magic numbers'' of electrons for a given system size or of atoms for a fixed electron density. The grand canonical BCS method essentially misses this feature. Possible experimental methods for observing such shell effects are discussed.Comment: 5 pages, 5 figure

Integrability and exact solution for coupled BCS systems associated with the su(4)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.Comment: 15 page

A research study of the prevalence of venereal disease among senior high-school boys and the attitude of the community toward venereal instruction

Not Available.Ralph S. RichardsonNot ListedNot ListedMaster of ScienceDepartment Not ListedCunningham Memorial library, Terre Haute, Indiana State University.isua-thesis-1940-richardson.pdfMastersTitle from document title page. Document formatted into pages: contains 98p. : ill. Includes appendix

Conformal Field Theory and the Exact Solution of the BCS Hamiltonian

We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k goes to -2. This theory has to be perturbed by an operator proportional to the inverse of the BCS coupling constant. Using the free field realization of this perturbed Wess-Zumino-Witten model, we derive the exact Richardson's wave function and the integrals of motion of the reduced BCS model in the saddle point approximation. The construction is reminiscent of the CFT approach to the Fractional Quantum Hall effect.Comment: 10 pages, RevTe

Shape of nanosize superconducting grains: Does it influence pairing characteristics?

The Richardson exact solution for the reduced BCS Hamiltonian is applied to examine how sensitive are the pairing characteristics (condensation energy, spectroscopic gap, parity gap) to a specific configuration of single-electron energy levels in nanosize metallic grains. Using single-electron energy spectra in parallelepiped-shaped potential boxes with various volumes and aspect ratios as a model of energy levels in grains, we show that this sensitivity is extremely high. Just due to such an extreme sensitivity, the detailed shape of grains cannot be detected through the pairing characteristics, averaged over an ensemble of grains, even in the case of relatively small size dispersion within this ensemble. We analyse the effect of the pairing interaction on the excited-level spacings in superconducting grains and comment on the influence of shape-dependent fluctuations in single-electron energy spectra on the possibility to reveal this effect through tunnelling measurements.Comment: 13 pages, 5 figures, to be published in Solid State Communications, E-mail addresses: [email protected], [email protected], [email protected]

Coronal disturbances and their effects on the dynamics of the heliosphere

The Sun blows out the solar wind which propagates into the interplanetary medium and forms the heliosphere about 100 AU across. The solar activity causes various types of time-dependent phenomena in the solar wind from long-lived corotating interaction regions to shorter on duration but more extreme events like coronal mass ejections. As these structures propagate outward from the Sun, they evolve and interact with each other and the ambient solar wind. Voyager 1 and 2 provided first unique in-situ measurements of these structures in the outer heliosphere. In particular, Voyager observations in the heliosheath, the outermost region of the heliosphere, showed highly variable plasma flows indicating effects of solar variations extending from the Sun to the heliosphere boundaries. Most surprisingly, Voyager 1 data shows shocks and pressure waves beyond the heliosphere in the interstellar medium. Important questions for the future Interstellar Probe mission are (1) how do the heliosphere boundaries respond to solar variations? (2) how do disturbances evolve in the heliosheath? and (3) how far does the Sun influence extend into the interstellar medium? This talk will review observations and recent modeling efforts demonstrating highly variable and dynamic nature of the global heliosphere in response to disturbances originated in the Sun's atmosphere.https://ui.adsabs.harvard.edu/abs/2019EPSC...13.1229P/abstractPublished versio

Quantum Entanglement and Order Parameter in a Paired Finite Fermi System

We study the pairing correlations in a finite Fermi system from quantum entanglement point of view. We investigate the relation between the order parameter, which has been introduced recently to describe both finite and infinite superconductors, and the concurrence. For a proper definition of the concurrence, we argue that a possible generalization of spin flip transformation is time reversal operation. While for a system with indefinite number of particles concurrence is a good measure of entanglement, for a finite system it does not distinguish between normal and superconducting states. We propose that the expectation value of the radial operator for the total pseudospin can be used to identify entanglement of pairing.Comment: submitted to Solid State Communications (the Festschrift in the honor of Prof. Salim Ciraci's 60th birthday

Chern-Simons theory and BCS superconductivity

We study the relationship between the holomorphic unitary connection of Chern-Simons theory with temporal Wilson lines and the Richardson's exact solution of the reduced BCS Hamiltonian. We derive the integrals of motion of the BCS model, their eigenvalues and eigenvectors as a limiting case of the Chern-Simons theory.Comment: 23 page

Superconducting fluctuations in small grains - the Universal Hamiltonian and the reduced BCS model

Small superconducting grains are discussed in the frameworks of both the reduced BCS Hamiltonian and the Universal Hamiltonian. It is shown that fluctuations of electrons in levels far from the Fermi energy dominate superconducting properties in small and ultrasmall grains. Experimental consequences related to the spin susceptibility and persistent currents of grains and rings with weak electron-electron interactions are discussed.Comment: Contribution to the proceedings of "Fluctuations and phase transitions in superconductors", Nazareth Ilit, Israel, June 10-14, 200