13,874 research outputs found
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
Pre-scission neutron multiplicity associated with the dynamical process in superheavy mass region
The fusion-fission process accompanied by neutron emission is studied in the
superheavy-mass region on the basis of the fluctuation-dissipation model
combined with a statistical model. The calculation of the trajectory or the
shape evolution in the deformation space of the nucleus with neutron emission
is performed. Each process (quasi-fission, fusion-fission, and deep
quasi-fission processes) has a characteristic travelling time from the point of
contact of colliding nuclei to the scission point. These dynamical aspects of
the whole process are discussed in terms of the pre-scission neutron
multiplicity, which depends on the time spent on each process. We have
presented the details of the characteristics of our model calculation in the
reactions Ca+Pb and Ca+Pu, and shown how the
structure of the distribution of pre-scission neutron multiplicity depends on
the incident energy.Comment: 19 pages, 12 figures, Accepted for publication in J. Phys.
Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory
In general, Whitham dynamics involves infinitely many parameters called
Whitham times, but in the context of N=2 supersymmetric Yang-Mills theory it
can be regarded as a finite system by restricting the number of Whitham times
appropriately. For example, in the case of SU(r+1) gauge theory without
hypermultiplets, there are r Whitham times and they play an essential role in
the theory. In this situation, the generating meromorphic 1-form of the Whitham
hierarchy on Seiberg-Witten curve is represented by a finite linear combination
of meromorphic 1-forms associated with these Whitham times, but it turns out
that there are various differential relations among these differentials. Since
these relations can be written only in terms of the Seiberg-Witten 1-form,
their consistency conditions are found to give the Picard-Fuchs equations for
the Seiberg-Witten periods.Comment: to be published in J. Math. Phys, revtex, 14 page
Bogoliubov quasiparticle spectra of the effective d-wave model for cuprate superconductivity
An exact-diagonalization technique on finite-size clusters is used to study
the ground state and excitation spectra of the two-dimensional effective
fermion model, a fictious model of hole quasiparticles derived from numerical
studies of the two-dimensional t-J model at low doping. We show that there is
actually a reasonable range of parameter values where the -wave
pairing of holes occurs and the low-lying excitation can be described by the
picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap
parameter of a size (where is the attractive
interaction between holes) is estimated at low doping levels. The paired state
gives way to the state of clustering of holes for some stronger attractions.Comment: 4 pages, RevTeX. Figures available upon request to
[email protected]. To be published in Phys. Rev.
Possibility of synthesizing doubly closed superheavy nucleus
The possibility of synthesizing a doubly magic superheavy nucleus,
, is investigated on the basis of fluctuation-dissipation
dynamics. In order to synthesize this nucleus, we must generate more
neutron-rich compound nuclei because of the neutron emissions from excited
compound nuclei. The compound nucleus has two advantages to
achieving a high survival probability. First, because of small neutron
separation energy and rapid cooling, the shell correction energy recovers
quickly. Secondly, owing to neutron emissions, the neutron number of the
nucleus approaches that of the double closed shell and the nucleus obtains a
large fission barrier. Because of these two effects, the survival probability
of does not decrease until the excitation energy MeV.
These properties lead to a rather high evaporation reside cross section.Comment: 5 pages, 6 figure
Dual WDVV Equations in N=2 Supersymmetric Yang-Mills Theory
This paper studies the dual form of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV)
equations in N=2 supersymmetric Yang-Mills theory by applying a duality
transformation to WDVV equations. The dual WDVV equations called in this paper
are non-linear differential equations satisfied by dual prepotential and are
found to have the same form with the original WDVV equations. However, in
contrast with the case of weak coupling calculus, the perturbative part of dual
prepotential itself does not satisfy the dual WDVV equations. Nevertheless, it
is possible to show that the non-perturbative part of dual prepotential can be
determined from dual WDVV equations, provided the perturbative part is given.
As an example, the SU(4) case is presented. The non-perturbative dual
prepotential derived in this way is consistent to the dual prepotential
obtained by D'Hoker and Phong.Comment: misprints are corrected, revtex, 10 page
Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity
We present an exact solution to the problem of the relativistic motion of 2
point masses in dimensional dilaton gravity. The motion of the bodies
is governed entirely by their mutual gravitational influence, and the spacetime
metric is likewise fully determined by their stress-energy. A Newtonian limit
exists, and there is a static gravitational potential. Our solution gives the
exact Hamiltonian to infinite order in the gravitational coupling constant.Comment: 6 pages, latex, 3 figure
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