1,466 research outputs found
Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations
The Hamiltonian approach to the theory of dual isomonodromic deformations is
developed within the framework of rational classical R-matrix structures on
loop algebras. Particular solutions to the isomonodromic deformation equations
appearing in the computation of correlation functions in integrable quantum
field theory models are constructed through the Riemann-Hilbert problem method.
The corresponding -functions are shown to be given by the Fredholm
determinant of a special class of integral operators.Comment: LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop:
Supersymmetric and Integrable Systems, University of Illinois, Chicago
Circle, June 12-14, 1997. To appear in: Springer Lecture notes in Physic
Generalized Kontsevich Model Versus Toda Hierarchy and Discrete Matrix Models
We represent the partition function of the Generalized Kontsevich Model (GKM)
in the form of a Toda lattice -function and discuss various implications
of non-vanishing "negative"- and "zero"-time variables: the appear to modify
the original GKM action by negative-power and logarithmic contributions
respectively. It is shown that so deformed -function satisfies the same
string equation as the original one. In the case of quadratic potential GKM
turns out to describe {\it forced} Toda chain hierarchy and, thus, corresponds
to a {\it discrete} matrix model, with the role of the matrix size played by
the zero-time (at integer positive points). This relation allows one to discuss
the double-scaling continuum limit entirely in terms of GKM, essentially
in terms of {\it finite}-fold integrals.Comment: 46
The Monodromy Matrices of the XXZ Model in the Infinite Volume Limit
We consider the XXZ model in the infinite volume limit with spin half quantum
space and higher spin auxiliary space. Using perturbation theory arguments, we
relate the half infinite transfer matrices of this class of models to certain
intertwiners introduced by Nakayashiki. We construct the
monodromy matrices, and show that the one with spin one auxiliary space gives
rise to the L operator.Comment: 19 page
New matrix model solutions to the Kac-Schwarz problem
We examine the Kac-Schwarz problem of specification of point in Grassmannian
in the restricted case of gap-one first-order differential Kac-Schwarz
operators. While the pair of constraints satisfying always
leads to Kontsevich type models, in the case of the
corresponding KP -functions are represented as more sophisticated matrix
integrals.Comment: 19 pages, latex, no figures, contribution to the proceedings of the
29th International Symposium Ahrenshoop on the Theory of Elementary
Particles, Buckow, German
Form factors of the XXZ model and the affine quantum group symmetry
We present new expressions of form factors of the XXZ model which satisfy
Smirnov's three axioms. These new form factors are obtained by acting the
affine quantum group to the known ones obtained
in our previous works. We also find the relations among all the new and known
form factors, i.e., all other form factors can be expressed as kind of
descendents of a special one.Comment: 11 pages, latex; Some explanation is adde
Bilinear structure and Schlesinger transforms of the -P and -P equations
We show that the recently derived (-) discrete form of the Painlev\'e VI
equation can be related to the discrete P, in particular if one
uses the full freedom in the implementation of the singularity confinement
criterion. This observation is used here in order to derive the bilinear forms
and the Schlesinger transformations of both -P and -P.Comment: 10 pages, Plain Te
Random Words, Toeplitz Determinants and Integrable Systems. I
It is proved that the limiting distribution of the length of the longest
weakly increasing subsequence in an inhomogeneous random word is related to the
distribution function for the eigenvalues of a certain direct sum of Gaussian
unitary ensembles subject to an overall constraint that the eigenvalues lie in
a hyperplane.Comment: 15 pages, no figure
Comultiplication in ABCD algebra and scalar products of Bethe wave functions
The representation of scalar products of Bethe wave functions in terms of the
Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important
role in the theory of completely integrable models. The proof in
\cite{Izergin87} and \cite{Korepin87} is based on the explicit expression for
the "senior" coefficient which was guessed in \cite{Izergin87} and then proven
to satisfy some recurrent relations, which determine it unambiguously. In this
paper we present an alternative proof based on the direct computation.Comment: 9 page
Annihilation poles of a Smirnov-type integral formula for solutions to quantum Knizhnik--Zamolodchikov equation
We consider the recently obtained integral representation of quantum
Knizhnik-Zamolodchikov equation of level 0. We obtain the condition for the
integral kernel such that these solutions satisfy three axioms for form factor
\'{a} la Smirnov. We discuss the relation between this integral representation
and the form factor of XXZ spin chain.Comment: 14 pages, latex, no figures
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