Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory

Instanton correction of prepotential of one-dimensional SL(2) Ruijsenaars model is presented with the help of Picard-Fuchs equation of Pakuliak-Perelomov type. It is shown that the instanton induced prepotential reduces to that of the SU(2) gauge theory coupled with a massive adjoint hypermultiplet.Comment: revtex, 15 pages, to be published in Journal of Mathematical Physic

Picard-Fuchs Ordinary Differential Systems in N=2 Supersymmetric Yang-Mills Theories

In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard-Fuchs ODEs. In contrast with the usual Picard-Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli and QCD scale parameter, which in the case of SU(2) is reminiscent of scaling relation of prepotential. On the other hand, in the case of the SU(3) theory, there are two kinds of ordinary differential equations, one of which is the equation directly constructed from periods and the other is derived from the SU(3) Picard-Fuchs equations in moduli derivatives identified with Appell's $F_4$ hypergeometric system, i.e., Burchnall's fifth order ordinary differential equation published in 1942. It is shown that four of the five independent solutions to the latter equation actually correspond to the four periods in the SU(3) gauge theory and the closed form of the remaining one is established by the SU(3) Picard-Fuchs ODE. The formula for this fifth solution is a new one.Comment: \documentstyle[12pt,preprint,aps,prb]{revtex}, to be published in J. Math. Phy

Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model

The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is observed that the time-dependent solutions of the derived dynamical systems obtained by the perturbation analysis become systematically closer to the results obtained by Monte Carlo simulations as the order of a perturbation series is increased. This systematic perturbation analysis also clarifies the existence of a dynamical scaling law, which provides a implication for a universal relation between a size scale and a time scale near the nonergodic transition.Comment: 17 pages, 7 figures, v2; results have been refined, v3; A figure has been modified, v4; results have been more refine

Potential Profiling of the Nanometer-Scale Charge Depletion Layer in n-ZnO/p-NiO Junction Using Photoemission Spectroscopy

We have performed a depth-profile analysis of an all-oxide p-n junction diode n-ZnO/p-NiO using photoemission spectroscopy combined with Ar-ion sputtering. Systematic core-level shifts were observed during the gradual removal of the ZnO overlayer, and were interpreted using a simple model based on charge conservation. Spatial profile of the potential around the interface was deduced, including the charge-depletion width of 2.3 nm extending on the ZnO side and the built-in potential of 0.54 eV