400 research outputs found
Bethe vectors of gl(3)-invariant integrable models, their scalar products and form factors
This short note corresponds to a talk given at "Lie Theory and Its
Applications in Physics", (Varna, Bulgaria, June 2013) and is based on joint
works with S. Belliard, S. Pakuliak and N. Slavnov, see arXiv:1206.4931,
arXiv:1207.0956, arXiv:1210.0768, arXiv:1211.3968 and arXiv:1312.1488.Comment: 15 page
Vertex operators for boundary algebras
We construct embeddings of boundary algebras B into ZF algebras A. Since it
is known that these algebras are the relevant ones for the study of quantum
integrable systems (with boundaries for B and without for A), this connection
allows to make the link between different approaches of the systems with
boundaries. The construction uses the well-bred vertex operators built
recently, and is classified by reflection matrices. It relies only on the
existence of an R-matrix obeying a unitarity condition, and as such can be
applied to any infinite dimensional quantum group.Comment: 11 pages, no figure, Latex2
Integrable systems with impurity
After reviewing some basic properties of RT algebras, which appear to be the
natural framework to deal with integrable systems in presence of an impurity,
we show how any integrable system (including these possessing translation
invariance) can be promoted to an integrable system with an impurity which can
reflect and transmit particles. The technics allows bulk translation invariant
-matrices while avoiding the no-go theorem stated recently about these
laters.
Presented at the Vth International workshop on Lie theory and its
applications in physics, Varna (Bulgaria), June 16-22, 2003Comment: 14 pages; Misprint in eq. (3.6) and (3.7) correcte
Yangian realisations from finite W algebras
We construct an algebra homomorphism between the Yangian Y(sl(n)) and the
finite W-algebras W(sl(np),n.sl(p)) for any p. We show how this result can be
applied to determine properties of the finite dimensional representations of
such W-algebras.Comment: 26 pages, Latex2
Direct computation of scattering matrices for general quantum graphs
We present a direct and simple method for the computation of the total
scattering matrix of an arbitrary finite noncompact connected quantum graph
given its metric structure and local scattering data at each vertex. The method
is inspired by the formalism of Reflection-Transmission algebras and quantum
field theory on graphs though the results hold independently of this formalism.
It yields a simple and direct algebraic derivation of the formula for the total
scattering and has a number of advantages compared to existing recursive
methods. The case of loops (or tadpoles) is easily incorporated in our method.
This provides an extension of recent similar results obtained in a completely
different way in the context of abstract graph theory. It also allows us to
discuss briefly the inverse scattering problem in the presence of loops using
an explicit example to show that the solution is not unique in general. On top
of being conceptually very easy, the computational advantage of the method is
illustrated on two examples of "three-dimensional" graphs (tetrahedron and
cube) for which other methods are rather heavy or even impractical.Comment: 20 pages, 4 figure
Generalized coordinate Bethe ansatz for non diagonal boundaries
We compute the spectrum and the eigenstates of the open XXX model with
non-diagonal (triangular) boundary matrices. Since the boundary matrices are
not diagonal, the usual coordinate Bethe ansatz does not work anymore, and we
use a generalization of it to solve the problem.Comment: 11 pages; References added and misprints correcte
Algebraic approach to multiple defects on the line and application to Casimir force
An algebraic framework for quantization in presence of arbitrary number of
point-like defects on the line is developed. We consider a scalar field which
interacts with the defects and freely propagates away of them. As an
application we compute the Casimir force both at zero and finite temperature.
We derive also the charge density in the Gibbs state of a complex scalar field
with defects. The example of two delta-defects is treated in detail.Comment: 24 pages, 10 figure
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