1,821 research outputs found
Isolated Horizon, Killing Horizon and Event Horizon
We consider space-times which in addition to admitting an isolated horizon
also admit Killing horizons with or without an event horizon. We show that an
isolated horizon is a Killing horizon provided either (1) it admits a
stationary neighbourhood or (2) it admits a neighbourhood with two independent,
commuting Killing vectors. A Killing horizon is always an isolated horizon. For
the case when an event horizon is definable, all conceivable relative locations
of isolated horizon and event horizons are possible. Corresponding conditions
are given.Comment: 14 pages, Latex, no figures. Some arguments tightened. To appear in
Class. Quant. Gra
A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation
The Hirota bilinear difference equation is generalized to discrete space of
arbitrary dimension. Solutions to the nonlinear difference equations can be
obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur
Solutions of a discretized Toda field equation for from Analytic Bethe Ansatz
Commuting transfer matrices of vertex models obey the
functional relations which can be viewed as an type Toda field equation
on discrete space time. Based on analytic Bethe ansatz we present, for
, a new expression of its solution in terms of determinants and
Pfaffians.Comment: Latex, 14 pages, ioplppt.sty and iopl12.sty assume
Classical Many-particle Clusters in Two Dimensions
We report on a study of a classical, finite system of confined particles in
two dimensions with a two-body repulsive interaction. We first develop a simple
analytical method to obtain equilibrium configurations and energies for few
particles. When the confinement is harmonic, we prove that the first transition
from a single shell occurs when the number of particles changes from five to
six. The shell structure in the case of an arbitrary number of particles is
shown to be independent of the strength of the interaction but dependent only
on its functional form. It is also independent of the magnetic field strength
when included. We further study the effect of the functional form of the
confinement potential on the shell structure. Finally we report some
interesting results when a three-body interaction is included, albeit in a
particular model.Comment: Minor corrections, a few references added. To appear in J. Phys:
Condensed Matte
Dual Resonance Model Solves the Yang-Baxter Equation
The duality of dual resonance models is shown to imply that the four point
string correlation function solves the Yang-Baxter equation. A reduction of
transfer matrices to symmetry is described by a restriction of the KP
function to Toda molecules.Comment: 10 pages, LaTe
A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models
We present a procedure in which known solutions to reflection equations for
interaction-round-a-face lattice models are used to construct new solutions.
The procedure is particularly well-suited to models which have a known fusion
hierarchy and which are based on graphs containing a node of valency . Among
such models are the Andrews-Baxter-Forrester models, for which we construct
reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe
A survey of Hirota's difference equations
A review of selected topics in Hirota's bilinear difference equation (HBDE)
is given. This famous 3-dimensional difference equation is known to provide a
canonical integrable discretization for most important types of soliton
equations. Similarly to the continuous theory, HBDE is a member of an infinite
hierarchy. The central point of our exposition is a discrete version of the
zero curvature condition explicitly written in the form of discrete
Zakharov-Shabat equations for M-operators realized as difference or
pseudo-difference operators. A unified approach to various types of M-operators
and zero curvature representations is suggested. Different reductions of HBDE
to 2-dimensional equations are considered. Among them discrete counterparts of
the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical
examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty
On the domain wall partition functions of level-1 affine so(n) vertex models
We derive determinant expressions for domain wall partition functions of
level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing
parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil
Pfaffian and Determinant Solutions to A Discretized Toda Equation for and
We consider a class of 2 dimensional Toda equations on discrete space-time.
It has arisen as functional relations in commuting family of transfer matrices
in solvable lattice models associated with any classical simple Lie algebra
. For and , we present the solution in terms of
Pfaffians and determinants. They may be viewed as Yangian analogues of the
classical Jacobi-Trudi formula on Schur functions.Comment: Plain Tex, 9 page
Complex Analysis of a Piece of Toda Lattice
We study a small piece of two dimensional Toda lattice as a complex dynamical
system. In particular the Julia set, which appears when the piece is deformed,
is shown analytically how it disappears as the system approaches to the
integrable limit.Comment: 17 pages, LaTe
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