120 research outputs found
A direct method for solving the generalized sine-Gordon equation II
The generalized sine-Gordon (sG) equation
was derived as an integrable generalization of the sG equation. In a previous
paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is
referred to as I, we developed a systematic method for solving the generalized
sG equation with . Here, we address the equation with . By
solving the equation analytically, we find that the structure of solutions
differs substantially from that of the former equation. In particular, we show
that the equation exhibits kink and breather solutions and does not admit
multi-valued solutions like loop solitons as obtained in I. We also demonstrate
that the equation reduces to the short pulse and sG equations in appropriate
scaling limits. The limiting forms of the multisoliton solutions are also
presented. Last, we provide a recipe for deriving an infinite number of
conservation laws by using a novel B\"acklund transformation connecting
solutions of the sG and generalized sG equations.Comment: To appear in J. Phys. A: Math. Theor. The first part of this paper
has been published in J. Phys. A: Math. Theor. 43 (2010) 10520
Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric t-J Model
We construct the Drinfeld twists (factorizing -matrices) for the
supersymmetric t-J model. Working in the basis provided by the -matrix (i.e.
the so-called -basis), we obtain completely symmetric representations of the
monodromy matrix and the pseudo-particle creation operators of the model. These
enable us to resolve the hierarchy of the nested Bethe vectors for the
invariant t-J model.Comment: 23 pages, no figure, Latex file, minor misprints are correcte
Yang--Baxter symmetry in integrable models: new light from the Bethe Ansatz solution
We show how any integrable 2D QFT enjoys the existence of infinitely many
non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry
algebra. These charges are generated by quantum monodromy operators and provide
a representation of deformed affine Lie algebras. We review and generalize
the work of de Vega, Eichenherr and Maillet on the bootstrap construction of
the quantum monodromy operators to the sine--Gordon (or massive Thirring)
model, where such operators do not possess a classical analogue. Within the
light--cone approach to the mT model, we explicitly compute the eigenvalues of
the six--vertex alternating transfer matrix \tau(\l) on a generic physical
state, through algebraic Bethe ansatz. In the thermodynamic limit \tau(\l)
turns out to be a two--valued periodic function. One determination generates
the local abelian charges, including energy and momentum, while the other
yields the abelian subalgebra of the (non--local) YB algebra. In particular,
the bootstrap results coincide with the ratio between the two determinations of
the lattice transfer matrix.Comment: 30 page
Quantization of the N=2 Supersymmetric KdV Hierarchy
We continue the study of the quantization of supersymmetric integrable KdV
hierarchies. We consider the N=2 KdV model based on the affine
algebra but with a new algebraic construction for the L-operator, different
from the standard Drinfeld-Sokolov reduction. We construct the quantum
monodromy matrix satisfying a special version of the reflection equation and
show that in the classical limit, this object gives the monodromy matrix of N=2
supersymmetric KdV system. We also show that at both the classical and the
quantum levels, the trace of the monodromy matrix (transfer matrix) is
invariant under two supersymmetry transformations and the zero mode of the
associated U(1) current.Comment: LaTeX2e, 12 page
Multiple integral representation for the trigonometric SOS model with domain wall boundaries
Using the dynamical Yang-Baxter algebra we derive a functional equation for
the partition function of the trigonometric SOS model with domain wall boundary
conditions. The solution of the equation is given in terms of a multiple
contour integral.Comment: 28 pages, v2: comments and references added, typos fixed, to appear
in NP
The Hyperbolic Heisenberg and Sigma Models in (1+1)-dimensions
Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg
Ferromagnet and sigma models are discussed in the context of topological
solutions classifiable by an integer `winding number'. Some explicit solutions
are presented and the existence of certain classes of such winding solutions
examined.Comment: 13 pages, 1 figure, Latex, personal style file included tensind.sty,
Proof in section 3 altered, no changes to conclusion
Factorization of the Universal R-matrix for
The factorization of the universal R-matrix corresponding to so called
Drinfeld Hopf structure is described on the example of quantum affine algebra
. As a result of factorization procedure we deduce certain
differential equations on the factors of the universal -matrix, which
allow to construct uniquely these factors in the integral form.Comment: 28 pages, LaTeX 2.09 using amssym.def and amssym.te
Resolution of the Nested Hierarchy for Rational sl(n) Models
We construct Drinfel'd twists for the rational sl(n) XXX-model giving rise to
a completely symmetric representation of the monodromy matrix. We obtain a
polarization free representation of the pseudoparticle creation operators
figuring in the construction of the Bethe vectors within the framework of the
quantum inverse scattering method. This representation enables us to resolve
the hierarchy of the nested Bethe ansatz for the sl(n) invariant rational
Heisenberg model. Our results generalize the findings of Maillet and Sanchez de
Santos for sl(2) models.Comment: 25 pages, no figure
Quantum integrable multi atom matter-radiation models with and without rotating wave approximation
New integrable multi-atom matter-radiation models with and without rotating
wave approximation (RWA) are constructed and exactly solved through algebraic
Bethe ansatz. The models with RWA are generated through ancestor model approach
in an unified way. The rational case yields the standard type of
matter-radiaton models, while the trigonometric case corresponds to their
q-deformations. The models without RWA are obtained from the elliptic case at
the Gaudin and high spin limit.Comment: 9 pages, no figure, talk presented in int. conf. NEEDS04 (Gallipoli,
Italy, July 2004
The Geometrodynamics of Sine-Gordon Solitons
The relationship between N-soliton solutions to the Euclidean sine-Gordon
equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is
investigated, with emphasis on the important role played by the dilaton in
determining the black hole geometry. We show how an N-soliton solution can be
used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and
construct the transformation to more standard ``Schwarzchild-like''
coordinates. For N=1 and 2, we find explicit closed form solutions to the
dilaton equations of motion in soliton coordinates, and find the relationship
between the soliton parameters and the black hole mass. Remarkably, the black
hole mass is non-negative for arbitrary soliton parameters. In the one-soliton
case the coordinates are shown to cover smoothly a region containing the whole
interior of the black hole as well as a finite neighbourhood outside the
horizon. A Hamiltonian analysis is performed for slicings that approach the
soliton coordinates on the interior, and it is shown that there is no boundary
contribution from the interior. Finally we speculate on the sine-Gordon
solitonic origin of black hole statistical mechanics.Comment: Latex, uses epsf, 30 pages, 6 figures include
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