1,299 research outputs found
The quantum bialgebra associated with the eight-vertex R-matrix
The quantum bialgebra related to the Baxter's eight-vertex R-matrix is found
as a quantum deformation of the Lie algebra of sl(2)-valued automorphic
functions on a complex torus.Comment: 4 page
The Lie algebra of sl(2)-valued automorphic functions on a torus
It is shown that the Lie algebra of the automorphic, meromorphic sl(2, C)
-valued functions on a torus is a geometric realization of a certain
infinite-dimensional finitely generated Lie algebra. In the trigonometric
limit, when the modular parameter of the torus goes to zero, the former Lie
algebra goes over into the sl(2,C) -valued loop algebra, while the latter one -
into the Lie algebra (sl(2)^)'/(centre) .Comment: 13 page
Spectral structure of a polycapillary lens shaped X-ray beam
Polycapillary X-ray optics is widely used in X-ray analysis techniques to create a small secondary source, for instance, or to deliver X-rays to the point of interest with minimum intensity losses [1]. The main characteristics of the analytical devices on its base are the size and divergence of the focused or translated beam. In this work, we used the photon-counting pixel detector ModuPIX to study the parameters for polycapillary focused X-ray tube radiation as well as the energy and spatial dependences of radiation at the focus. We have characterized the high-speed spectral camera ModuPIX, which is a single Timepix device with a fast parallel readout allowing up to 850 frames per second with 256•256 pixels and a 55 [mu]m pitch defined by the frame frequency. By means of the silicon monochromator the energy response function is measured in clustering mode by the energy scan over total X-ray tube spectrum
The Yangian of sl(n|m) and the universal R-matrix
In this paper we study Yangians of sl(n|m) superalgebras. We derive the
universal R-matrix and evaluate it on the fundamental representation obtaining
the standard Yang R-matrix with unitary dressing factors. For m=0, we directly
recover up to a CDD factor the well-known S-matrices for relativistic
integrable models with su(N) symmetry. Hence, the universal R-matrix found
provides an abstract plug-in formula, which leads to results obeying
fundamental physical constraints: crossing symmetry, unitrarity and the
Yang-Baxter equation. This implies that the Yangian double unifies all desired
symmetries into one algebraic structure. In particular, our analysis is valid
in the case of sl(n|n), where one has to extend the algebra by an additional
generator leading to the algebra gl(n|n). We find two-parameter families of
scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure
Collective Field Description of Spin Calogero-Sutherland Models
Using the collective field technique, we give the description of the spin
Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be
applicable for arbitrary coupling constant and provides the bosonized
Hamiltonian of the spin CSM. The boson Fock space can be identified with the
Hilbert space of the spin CSM in the large limit. We show that the
eigenstates corresponding to the Young diagram with a single row or column are
represented by the vertex operators. We also derive a dual description of the
Hamiltonian and comment on the construction of the general eigenstates.Comment: 14 pages, one figure, LaTeX, with minor correction
Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
Level statistics is discussed for XXZ spin chains with discrete symmetries
for some values of the next-nearest-neighbor (NNN) coupling parameter. We show
how the level statistics of the finite-size systems depends on the NNN coupling
and the XXZ anisotropy, which should reflect competition among quantum chaos,
integrability and finite-size effects. Here discrete symmetries play a central
role in our analysis. Evaluating the level-spacing distribution, the spectral
rigidity and the number variance, we confirm the correspondence between
non-integrability and Wigner behavior in the spectrum. We also show that
non-Wigner behavior appears due to mixed symmetries and finite-size effects in
some nonintegrable cases.Comment: 19 pages, 6 figure
The structure of quotients of the Onsager algebra by closed ideals
We study the Onsager algebra from the ideal theoretic point of view. A
complete classification of closed ideals and the structure of quotient algebras
are obtained. We also discuss the solvable algebra aspect of the Onsager
algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio
sl(N) Onsager's Algebra and Integrability
We define an analog of Onsager's Algebra through a finite set of
relations that generalize the Dolan Grady defining relations for the original
Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be
isomorphic to a fixed point subalgebra of Loop Algebra with respect
to a certain involution. As the consequence of the generalized Dolan Grady
relations a Hamiltonian linear in the generators of Onsager's Algebra
is shown to posses an infinite number of mutually commuting integrals of
motion
Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A
We are interested in the structure of the crystal graph of level Fock
spaces representations of . Since
the work of Shan [26], we know that this graph encodes the modular branching
rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it
appears to be closely related to the Harish-Chandra branching graph for the
appropriate finite unitary group, according to [8]. In this paper, we make
explicit a particular isomorphism between connected components of the crystal
graphs of Fock spaces. This so-called "canonical" crystal isomorphism turns out
to be expressible only in terms of: - Schensted's classic bumping procedure, -
the cyclage isomorphism defined in [13], - a new crystal isomorphism, easy to
describe, acting on cylindric multipartitions. We explain how this can be seen
as an analogue of the bumping algorithm for affine type . Moreover, it
yields a combinatorial characterisation of the vertices of any connected
component of the crystal of the Fock space
Conformal field theory and edge excitations for the principal series of quantum Hall fluids
Motivated by recent experimental results, we reconsider the theory of the
edge excitations for the fractional Hall effect at filling factors
. We propose to modify the standard edge
theory for this series by introducing twist fields which change the boundary
conditions of the bosonic fields and simulate the effect of fractions of flux
quanta . This has the effect of removing the conserved charges
associated to the neutral modes while keeping the right statistics of the
particles. The Green function of the electron in presence of twists decays at
long distance with an exponent varying continuously with .Comment: 5 pages, latex; typos corrected and some references adde
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