11,466 research outputs found
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
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
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