132 research outputs found
Solutions of the Generic Non-Compact Weyl Equation
In this paper, solutions of the generic non-compact Weyl equation are
obtained. In particular, by identifying a suitable similarity transformation
and introducing a non-trivial change of variables we are able to implement
azimuthal dependence on the solutions of the diagonal non-compact Weyl
equation. We also discuss some open questions related to the construction of
infinite BPS monopole configurations.Comment: 12 pages, Latex. Few extra comments and a reference adde
Non-diagonal reflection for the non-critical XXZ model
The most general physical boundary -matrix for the open XXZ spin chain in
the non-critical regime () is derived starting from the bare
Bethe ansazt equations. The boundary -matrix as expected is expressed in
terms of -functions. In the isotropic limit corresponding results for
the open XXX chain are also reproduced.Comment: 8 pages Late
Direct Calculation of Breather S Matrices
We formulate a systematic Bethe-Ansatz approach for computing bound-state
(``breather'') S matrices for integrable quantum spin chains. We use this
approach to calculate the breather boundary S matrix for the open XXZ spin
chain with diagonal boundary fields. We also compute the soliton boundary S
matrix in the critical regime.Comment: 23 pages, LaTeX, 1 eps figur
Fusion and Analytical Bethe Ansatz for the A_{\n-1}^{(1)} Open Spin Chain
We generalise the fusion procedure for the A_{\n-1}^{(1)} open spin chain (\n>2) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the A_{\n-1}^{(1)} open spin chain with U_{q} (SU(\n)) symmetry by means of the analytical Bethe ansatz method. Our results coincide with the known ones obtained by means of the nested Bethe ansatz
New reflection matrices for the U_q(gl(m|n)) case
We examine super symmetric representations of the B-type Hecke algebra. We
exploit such representations to obtain new non-diagonal solutions of the
reflection equation associated to the super algebra U_q(gl(m|n)). The boundary
super algebra is briefly discussed and it is shown to be central to the super
symmetric realization of the B-type Hecke algebraComment: 13 pages, Latex. A few alterations regarding the representations. A
reference adde
On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
Motivated by a study of the crossing symmetry of the `gemini' representation
of the affine Hecke algebra we give a construction for crossing tensor space
representations of ordinary Hecke algebras. These representations build
solutions to the Yang--Baxter equation satisfying the crossing condition (that
is, integrable quantum spin chains). We show that every crossing representation
of the Temperley--Lieb algebra appears in this construction, and in particular
that this construction builds new representations. We extend these to new
representations of the blob algebra, which build new solutions to the Boundary
Yang--Baxter equation (i.e. open spin chains with integrable boundary
conditions).
We prove that the open spin chain Hamiltonian derived from Sklyanin's
commuting transfer matrix using such a solution can always be expressed as the
representation of an element of the blob algebra, and determine this element.
We determine the representation theory (irreducible content) of the new
representations and hence show that all such Hamiltonians have the same
spectrum up to multiplicity, for any given value of the algebraic boundary
parameter. (A corollary is that our models have the same spectrum as the open
XXZ chain with nondiagonal boundary -- despite differing from this model in
having reference states.) Using this multiplicity data, and other ideas, we
investigate the underlying quantum group symmetry of the new Hamiltonians. We
derive the form of the spectrum and the Bethe ansatz equations.Comment: 43 pages, multiple figure
Selected Topics in Classical Integrability
Basic notions regarding classical integrable systems are reviewed. An
algebraic description of the classical integrable models together with the zero
curvature condition description is presented. The classical r-matrix approach
for discrete and continuum classical integrable models is introduced. Using
this framework the associated classical integrals of motion and the
corresponding Lax pair are extracted based on algebraic considerations. Our
attention is restricted to classical discrete and continuum integrable systems
with periodic boundary conditions. Typical examples of discrete (Toda chain,
discrete NLS model) and continuum integrable models (NLS, sine-Gordon models
and affine Toda field theories) are also discussed.Comment: 40 pages, Latex. A few typos correcte
Partial differential systems with nonlocal nonlinearities: Generation and solutions
We develop a method for generating solutions to large classes of evolutionary
partial differential systems with nonlocal nonlinearities. For arbitrary
initial data, the solutions are generated from the corresponding linearized
equations. The key is a Fredholm integral equation relating the linearized flow
to an auxiliary linear flow. It is analogous to the Marchenko integral equation
in integrable systems. We show explicitly how this can be achieved through
several examples including reaction-diffusion systems with nonlocal quadratic
nonlinearities and the nonlinear Schrodinger equation with a nonlocal cubic
nonlinearity. In each case we demonstrate our approach with numerical
simulations. We discuss the effectiveness of our approach and how it might be
extended.Comment: 4 figure
Introduction to Quantum Integrability
In this article we review the basic concepts regarding quantum integrability.
Special emphasis is given on the algebraic content of integrable models. The
associated algebras are essentially described by the Yang-Baxter and boundary
Yang-Baxter equations depending on the choice of boundary conditions. The
relation between the aforementioned equations and the braid group is briefly
discussed. A short review on quantum groups as well as the quantum inverse
scattering method (algebraic Bethe ansatz) is also presented.Comment: 56 pages, Latex. A few typos correcte
- …