Meissner state in finite superconducting cylinders with uniform applied magnetic field

We study the magnetic response of superconductors in the presence of low values of a uniform applied magnetic field. We report measurements of DC magnetization and AC magnetic susceptibility performed on niobium cylinders of different length-to-radius ratios, which show a dramatic enhance of the initial magnetization for thin samples, due to the demagnetizing effects. The experimental results are analyzed by applying a model that calculates the magnetic response of the superconductor, taking into account the effects of the demagnetizing fields. We use the results of magnetization and current and field distributions of perfectly diamagnetic cylinders to discuss the physics of the demagnetizing effects in the Meissner state of type-II superconductors.Comment: Accepted to be published in Phys. Rev. B; 15 pages, 7 ps figure

Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in d=3d=3 based on spacetime norms

We derive the defocusing cubic Gross-Pitaevskii (GP) hierarchy in dimension $d=3$, from an $N$-body Schr\"{o}dinger equation describing a gas of interacting bosons in the GP scaling, in the limit $N\rightarrow\infty$. The main result of this paper is the proof of convergence of the corresponding BBGKY hierarchy to a GP hierarchy in the spaces introduced in our previous work on the well-posedness of the Cauchy problem for GP hierarchies, \cite{chpa2,chpa3,chpa4}, which are inspired by the solutions spaces based on space-time norms introduced by Klainerman and Machedon in \cite{klma}. We note that in $d=3$, this has been a well-known open problem in the field. While our results do not assume factorization of the solutions, consideration of factorized solutions yields a new derivation of the cubic, defocusing nonlinear Schr\"odinger equation (NLS) in $d=3$.Comment: 44 pages, AMS Late

Asymptotics of basic Bessel functions and q-Laguerre polynomials

AbstractWe establish a large n complete asymptotic expansion for q-Laguerre polynomials and a complete asymptotic expansion for a q-Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907)

Tau-Function Constructions of the Recurrence Coefficients of Orthogonal Polynomials

AbstractIn this paper we compute the recurrence coefficients of orthogonal polynomials using τ-function techniques. It is shown that for polynomials orthogonal with respect to positive weight functions on a noncompact interval, the recurrence coefficient can be expressed as the change in the chemical potential which, for sufficiently largeNis the second derivative of the free energy with respect toN, the particle number. We give three examples using this technique: Freud weights, Erdős weights, and weak exponential weights

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.Comment: 50 pages;7 figure

Sequential pivotal mechanisms for public project problems

It is well-known that for several natural decision problems no budget balanced Groves mechanisms exist. This has motivated recent research on designing variants of feasible Groves mechanisms (termed as `redistribution of VCG (Vickrey-Clarke-Groves) payments') that generate reduced deficit. With this in mind, we study sequential mechanisms and consider optimal strategies that could reduce the deficit resulting under the simultaneous mechanism. We show that such strategies exist for the sequential pivotal mechanism of the well-known public project problem. We also exhibit an optimal strategy with the property that a maximal social welfare is generated when each player follows it. Finally, we show that these strategies can be achieved by an implementation in Nash equilibrium.Comment: 19 pages. The version without the appendix will appear in the Proc. 2nd International Symposium on Algorithmic Game Theory, 200

On the Rigorous Derivation of the 3D Cubic Nonlinear Schr\"odinger Equation with A Quadratic Trap

We consider the dynamics of the 3D N-body Schr\"{o}dinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N^{3{\beta}-1}V(N^{{\beta}}x). We justify the mean-field approximation and offer a rigorous derivation of the 3D cubic NLS with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon [30] for {\beta} in (0,2/7] by adapting and simplifying an argument in Chen and Pavlovi\'c [7] which solves the problem for {\beta} in (0,1/4) in the absence of a trap.Comment: Revised according to the referee report. Accepted to appear in Archive for Rational Mechanics and Analysi

Glueball plus Pion Production in Photon-Photon Collisions.

We here compute the reaction $\gamma \; \gamma \rightarrow G \; \pi^{0}$ for various glueball candidates $G$ and their assumed quantum states, using a non-relativistic gluon bound-state model for the glueball.Comment: To appear in Zeit. fur Phys. C; Plain Latex file, 16 pages; 5 figures appended as a uuencoded postscript file

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

Fermi super-Tonks-Girardeau state for attractive Fermi gases in an optical lattice

We demonstrate that a kind of highly excited state of strongly attractive Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in the spin-1/2 Fermi optical lattice system by a sudden switch of interaction from the strongly repulsive regime to the strongly attractive regime. In contrast to the ground state of the attractive Hubbard model, such a state is the lowest scattering state with no pairing between attractive fermions. With the aid of Bethe-ansatz method, we calculate energies of both the Fermi Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2 ultracold fermions and show that both energies approach to the same limit as the strength of the interaction goes to infinity. By exactly solving the quench dynamics of the Hubbard model, we demonstrate that the Fermi super-Tonks-Girardeau state can be transferred from the initial repulsive ground state very efficiently. This allows the experimental study of properties of Fermi super-Tonks-Girardeau gas in optical lattices.Comment: 7 pages, 7 figure