13,105 research outputs found
Schlesinger transformations for elliptic isomonodromic deformations
Schlesinger transformations are discrete monodromy preserving symmetry
transformations of the classical Schlesinger system. Generalizing well-known
results from the Riemann sphere we construct these transformations for
isomonodromic deformations on genus one Riemann surfaces. Their action on the
system's tau-function is computed and we obtain an explicit expression for the
ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2
Critical Properties of the transition between the Haldane phase and the large-D phase of the spin-1/2 ferromagnetic-antiferromagnetic Heisenberg chain with on-site anisotropy"
We analytically study the ground-state quantum phase transition between the
Haldane phase and the large- (LD) phase of the
ferromagnetic-antiferromagnetic alternating Heisenberg chain with on-site
anisotropy. We transform this model into a generalized version of the
alternating antiferromagnetic Heisenberg model with anisotropy. In the
transformed model, the competition between the transverse and longitudinal bond
alternations yields the Haldane-LD transition. Using the bosonization method,
we show that the critical exponents vary continuously on the Haldane-LD
boundary. Our scaling relations between critical exponents very well explains
the numerical results by Hida.Comment: text 12 pages (Plain TeX), LaTeX sourse files of a table and a figure
on reques
Making Clean Energy with a Kerr Black Hole: a Tokamak Model for Gamma-Ray Bursts
In this paper we present a model for making clean energy with a Kerr black
hole. Consider a Kerr black hole with a dense plasma torus spinning around it.
A toroidal electric current flows on the surface of the torus, which generates
a poloidal magnetic field outside the torus. On the surface of the tours the
magnetic field is parallel to the surface. The closed magnetic field lines
winding around the torus compress and confine the plasma in the torus, as in
the case of tokamaks. Though it is unclear if such a model is stable, we look
into the consequences if the model is stable. If the magnetic field is strong
enough, the baryonic contamination from the plasma in the torus is greatly
suppressed by the magnetic confinement and a clean magnetosphere of
electron-positron pairs is built up around the black hole. Since there are no
open magnetic field lines threading the torus and no accretion, the power of
the torus is zero. If some magnetic field lines threading the black hole are
open and connect with loads, clean energy can be extracted from the Kerr black
hole by the Blandford-Znajek mechanism.
The model may be relevant to gamma-ray bursts. The energy in the Poynting
flux produced by the Blandford-Znajek mechanism is converted into the kinetic
energy of the electron-positron pairs in the magnetosphere around the black
hole, which generates two oppositely directed jets of electron-positron pairs
with super-high bulk Lorentz factors. The jets collide and interact with the
interstellar medium, which may produce gamma-ray bursts and the afterglows.Comment: 14 pages, 1 figure, accepted by Ap
Formal Relation among Various Hermitian and non-Hermitian Effective Interactions
A general definition of the model-space effective interaction is given. The
energy-independent effective hamiltonians derived in a time-independent way are
classified systematically.Comment: To appear in IJMPE; Proceedings of "Blueprints for the Nucleus,"
Istanbul, Turkey, May 200
Tuning the spin dynamics of kagome systems
Despite the conceptional importance of realizing spin liquids in solid states
only few compounds are known. On the other side the effect of lattice
distortions and anisotropies on the magnetic exchange topology and the
fluctuation spectrum are an interesting problem. We compare the excitation
spectra of the two s=1/2 kagome lattice compounds volborthite and vesignieite
using Raman scattering. We demonstrate that even small modifications of the
crystal structure may have a huge effect on the phonon spectrum and low
temperature properties.Comment: 3 pages, 2 figure
A -anaolg of the sixth Painlev\'e equation
A -difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of -hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected
A remark on the Hankel determinant formula for solutions of the Toda equation
We consider the Hankel determinant formula of the functions of the
Toda equation. We present a relationship between the determinant formula and
the auxiliary linear problem, which is characterized by a compact formula for
the functions in the framework of the KP theory. Similar phenomena that
have been observed for the Painlev\'e II and IV equations are recovered. The
case of finite lattice is also discussed.Comment: 14 pages, IOP styl
Spin Gap of S=1/2 Heisenberg Model on Distorted Diamond Chain
We study the spin gap of the S=1/2 Heisenberg model on the distorted diamond
chain, which is recently proposed to represent magnetic properties of Cu_3 Cl_6
(H_2 O)_2 2H_8 C_4 SO_2. This model is composed of stacked trimers and has
three kinds of exchange interactions J_1, J_2 and J_3. Using the numerical
diagonalization, we obtain a contour map of the spin gap in the J_2/J_1-J_3/J_1
plane. We argue possible values of the exchange constants based on the contour
map and the observed value of the spin gap.Comment: 2 pages, 4 figure
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
Transverse radiation force in a tailored optical fiber
We show, by means of simple model calculations, how a weak laser beam sent
through an optical fiber exerts a transverse radiation force if there is an
azimuthal asymmetry present in the fiber such that one side has a slightly
different refractive index than the other. The refractive index difference
needs only to be very small, of order , in order to produce
an appreciable transverse displacement of order 10 microns. We argue that the
effect has probably already been seen in a recent experiment of She et al.
[Phys. Rev. Lett. 101, 243601 (2008)], and we discuss correspondence between
these observations and the theory presented. The effect could be used to bend
optical fibers in a predictable and controlled manner and we propose that it
could be useful for micron-scale devices.Comment: 4 pages, 3 figures. Accepted for publication as Rapid Communication
in Phys. Rev.
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