10,488 research outputs found
Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations
We develop the theory of irregular conformal blocks of the Virasoro algebra.
In previous studies, expansions of irregular conformal blocks at regular
singular points were obtained as degeneration limits of regular conformal
blocks; however, such expansions at irregular singular points were not clearly
understood. This is because precise definitions of irregular vertex operators
had not been provided previously. In this paper, we present precise definitions
of irregular vertex operators of two types and we prove that one of our vertex
operators exists uniquely. Then, we define irregular conformal blocks with at
most two irregular singular points as expectation values of given irregular
vertex operators. Our definitions provide an understanding of expansions of
irregular conformal blocks and enable us to obtain expansions at irregular
singular points.
As an application, we propose conjectural formulas of series expansions of
the tau functions of the fifth and fourth Painlev\'e equations, using
expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page
Rotation Curves of Spiral Galaxies and Large Scale Structure of Universe under Generalized Einstein Action
We consider an addition of the term which is a square of the scalar curvature
to the Einstein-Hilbert action. Under this generalized action, we attempt to
explain i) the flat rotation curves observed in spiral galaxies, which is
usually attributed to the existence of dark matter, and ii) the contradicting
observations of uniform cosmic microwave background and non-uniform galaxy
distributions against redshift. For the former, we attain the flatness of
velocities, although the magnitudes remain about half of the observations. For
the latter, we obtain a solution with oscillating Hubble parameter under
uniform mass distributions. This solution leads to several peaks of galaxy
number counts as a function of redshift with the first peak corresponding to
the Great Wall.Comment: 16 page
A generalization of determinant formulas for the solutions of Painlev\'e II and XXXIV equations
A generalization of determinant formulas for the classical solutions of
Painlev\'e XXXIV and Painlev\'e II equations are constructed using the
technique of Darboux transformation and Hirota's bilinear formalism. It is
shown that the solutions admit determinant formulas even for the transcendental
case.Comment: 20 pages, LaTeX 2.09(IOP style), submitted to J. Phys.
Magnetization plateaus in antiferromagnetic-(ferromagnetic)_{n} polymerized S=1/2 XXZ chains
The plateau-non-plateau transition in the
antiferromagnetic-(ferromagnetic) polymerized XXZ chains under
the magnetic field is investigated. The universality class of this transition
belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points
are determined by level spectroscopy analysis of the numerical diagonalization
data for where is the size of a unit cell.
It is found that the critical strength of ferromagnetic coupling decreases with
for small but increases for larger enough . It is also found that
the plateau for large is wide enough for moderate values of exchange
coupling so that it should be easily observed experimentally. This is in
contrast to the plateaus for chains which are narrow for a wide range
of exchange coupling even away from the critical point
Metal-Insulator Transition and Spin Degree of Freedom in Silicon 2D Electron Systems
Magnetotransport in 2DES's formed in Si-MOSFET's and Si/SiGe quantum wells at
low temperatures is reported. Metallic temperature dependence of resistivity is
observed for the n-Si/SiGe sample even in a parallel magnetic field of 9T,
where the spins of electrons are expected to be polarized completely.
Correlation between the spin polarization and minima in the diagonal
resistivity observed by rotating the samples for various total strength of the
magnetic field is also investigated.Comment: 3 pages, RevTeX, 4 eps-figures, conference paper (EP2DS-13
Anomalous magnetization process in frustrated spin ladders
We study, at T=0, the anomalies in the magnetization curve of the S=1 two-leg
ladder with frustrated interactions. We focus mainly on the existence of the
M=\Ms/2 plateau, where \Ms is the saturation magnetization. We use
analytical methods (degenerate perturbation theory and non-Abelian
bosonization) as well as numerical methods (level spectroscopy and density
matrix renormalization group), which lead to the consistent conclusion with
each other. We also touch on the M=\Ms/4 and M=(3/4)\Ms plateaux and cusps.Comment: 4 pages, 7 figures (embedded), Conference paper (Highly Frustrated
Magnetism 2003, 26-30th August 2003, Grenoble, France
Painleve equations from Darboux chains - Part 1: P3-P5
We show that the Painleve equations P3-P5 can be derived (in a unified way)
from a periodic sequence of Darboux transformations for a Schrodinger problem
with quadratic eigenvalue dependency. The general problem naturally divides
into three different branches, each described by an infinite chain of
equations. The Painleve equations are obtained by closing the chain
periodically at the lowest nontrivial level(s). The chains provide ``symmetric
forms'' for the Painleve equations, from which Hirota bilinear forms and Lax
pairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5,
while P6 will be studied in Part 2.Comment: 23 pages, 1 reference added + minor change
Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation
We investigate a non-equilibrium reaction-diffusion model and equivalent
ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The
exact energy spectrum and the n-point hole correlations are considered with the
help of the Jordan-Wigner fermionization and the inter-particle distribution
function method. Although the Hamiltonian has no explicit translational
symmetry, the translational invariance is recovered after long time due to the
diffusion. We see the scaling relations for the concentration and the two-point
function in finite size analysis.Comment: 7 pages, LaTeX file, to appear in J. Phys. A: Math. and Ge
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