7,627 research outputs found
-analog of the XXZ chain with a boundary
We study analog of the XXZ spin chain with a boundary
magnetic field h. We construct explicit bosonic formulas of the vacuum vector
and the dual vacuum vector with a boundary magnetic field. We derive integral
formulas of the correlation functions.Comment: 24 pages, LaTEX2
The Integrals of Motion for the Deformed W-Algebra II: Proof of the commutation relations
We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra , and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th
birthda
The R-Mode Oscillations in Relativistic Rotating Stars
The axial mode oscillations are examined for relativistic rotating stars with
uniform angular velocity. Using the slow rotation formalism and the Cowling
approximation, we have derived the equations governing the r-mode oscillations
up to the second order with respect to the rotation. In the lowest order, the
allowed range of the frequencies is determined, but corresponding spatial
function is arbitrary. The spatial function can be decomposed in non-barotropic
region by a set of functions associated with the differential equation of the
second-order corrections. The equation however becomes singular in barotropic
region, and a single function can be selected to describe the spatial
perturbation of the lowest order. The frame dragging effect among the
relativistic effects may be significant, as it results in rather broad spectrum
of the r-mode frequency unlike in the Newtonian first-order calculation.Comment: 19 pages, 4 figures, AAS LaTeX, Accepted for publication in The
Astrophysical Journa
Vertex operator approach for form factors of Belavin's -symmetric model
Belavin's -symmetric model is considered on the
basis of bosonization of vertex operators in the model and
vertex-face transformation. Free field representations of nonlocal tail
operators are constructed for off diagonal matrix elements with respect to the
ground state sectors. As a result, integral formulae for form factors of any
local operators in the -symmetric model can be
obtained, in principle.Comment: 24 pages, 4 figures, published in J. Phys. A: Math. Theor. 43 (2010)
085202. For the next thirty days from Feb 5 2010, the full text of the
article will be completely free to access through our 'This Month's Papers'
service (www.iop.org/journals/thismonth), helping you to benefit from maximum
visibilit
The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations
We revisit the question of the imposition of initial data representing
astrophysical gravitational perturbations of black holes. We study their
dynamics for the case of nonrotating black holes by numerically evolving the
Teukolsky equation in the time domain. In order to express the Teukolsky
function Psi explicitly in terms of hypersurface quantities, we relate it to
the Moncrief waveform phi_M through a Chandrasekhar transformation in the case
of a nonrotating black hole. This relation between Psi and phi_M holds for any
constant time hypersurface and allows us to compare the computation of the
evolution of Schwarzschild perturbations by the Teukolsky and by the Zerilli
and Regge-Wheeler equations. We explicitly perform this comparison for the
Misner initial data in the close limit approach. We evolve numerically both,
the Teukolsky (with the recent code of Ref. [1]) and the Zerilli equations,
finding complete agreement in resulting waveforms within numerical error. The
consistency of these results further supports the correctness of the numerical
code for evolving the Teukolsky equation as well as the analytic expressions
for Psi in terms only of the three-metric and the extrinsic curvature.Comment: 14 pages, 7 Postscript figures, to appear in Phys. Rev.
- …