589 research outputs found
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
Services rendus par les foraminifĂšres benthiques dans lâĂ©tude de lâinfluence des forçages naturels (e.g. changement climatique) et anthropiques sur lâĂ©cosystĂšme estuarien. Exemple de la Loire.
Due to its intermediate position between ocean and continent, estuary is located in the heart of the economic, social and cultural activities. Awareness of the need to manage this vulnerable environment, has led in recent years, to an increase in surveillance activities of the environmental quality. Physico-chemical methods, although dominant and indispensable, reach their limits as a tool for environmental management. This is why other ways are being explored, such as evaluating the environmental quality by bio-indicators. It is in this perspective that SEMHABEL project is subscribed (Suivi Environnemental des Micro-HAbitats Benthiques de lâEstuaire de la Loire - Plan Loire Grandeur Nature 2007-2013 - FEDER). This is the first study in the Loire incorporating the use of benthic foraminifera as a new biological approach. Following a sampling cruise in September 2012, 320 samples of surface sediments were collected from Nantes to de Saint-Gildas. The data obtained allowed to represent and analyze the spatial distribution of communities of benthic foraminifera, along the upstream-downstream continuum and following geochemical and sedimentary evolutions. These results are the first support for the establishment of a database that will allow a better understanding of the actual functioning of this ecosystem. Ultimately, we hope to assess the evolution of the estuarine ecosystem according to climate change and catchment area management and to develop a biotic index for routine monitoring of the health of the estuary
A reduced model for shock and detonation waves. II. The reactive case
We present a mesoscopic model for reactive shock waves, which extends a
previous model proposed in [G. Stoltz, Europhys. Lett. 76 (2006), 849]. A
complex molecule (or a group of molecules) is replaced by a single
mesoparticle, evolving according to some Dissipative Particle Dynamics.
Chemical reactions can be handled in a mean way by considering an additional
variable per particle describing a rate of reaction. The evolution of this rate
is governed by the kinetics of a reversible exothermic reaction. Numerical
results give profiles in qualitative agreement with all-atom studies
Current Algebra of Super WZNW Models
We derive the current algebra of supersymmetric principal chiral models with
a Wess-Zumino term. At the critical point one obtains two commuting super
Kac-Moody algebra as expected, but in general there are intertwining fields
connecting both right and left sectors, analogously to the bosonic case.
Moreover, in the present supersymmetric extension we have a quadratic algebra,
rather than an affine Lie algebra, due to the mixing between bosonic and
fermionic fields since the purely fermionic sector displays a Lie algebra as
well.Comment: 13 page
Bicrossed products for finite groups
We investigate one question regarding bicrossed products of finite groups
which we believe has the potential of being approachable for other classes of
algebraic objects (algebras, Hopf algebras). The problem is to classify the
groups that can be written as bicrossed products between groups of fixed
isomorphism types. The groups obtained as bicrossed products of two finite
cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor
Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
We compute all dynamical spin-spin correlation functions for the spin-1/2
anisotropic Heisenberg model in the gapless antiferromagnetic regime,
using numerical sums of exact determinant representations for form factors of
spin operators on the lattice. Contributions from intermediate states
containing many particles and string (bound) states are included. We present
modified determinant representations for the form factors valid in the general
case with string solutions to the Bethe equations. Our results are such that
the available sum rules are saturated to high precision. We Fourier transform
our results back to real space, allowing us in particular to make a comparison
with known exact formulas for equal-time correlation functions for small
separations in zero field, and with predictions for the zero-field asymptotics
from conformal field theory.Comment: 14 page
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
Drinfeld Twists and Symmetric Bethe Vectors of Supersymmetric Fermion Models
We construct the Drinfeld twists (factorizing -matrices) of the
-invariant fermion model. Completely symmetric representation of the
pseudo-particle creation operators of the model are obtained in the basis
provided by the -matrix (the -basis). We resolve the hierarchy of the
nested Bethe vectors in the -basis for the supersymmetric model.Comment: Latex File, 24 pages, no figure, some misprints are correcte
The classical R-matrix of AdS/CFT and its Lie dialgebra structure
The classical integrable structure of Z_4-graded supercoset sigma-models,
arising in the AdS/CFT correspondence, is formulated within the R-matrix
approach. The central object in this construction is the standard R-matrix of
the Z_4-twisted loop algebra. However, in order to correctly describe the Lax
matrix within this formalism, the standard inner product on this twisted loop
algebra requires a further twist induced by the Zhukovsky map, which also plays
a key role in the AdS/CFT correspondence. The non-ultralocality of the
sigma-model can be understood as stemming from this latter twist since it leads
to a non skew-symmetric R-matrix.Comment: 22 pages, 2 figure
Lattice Gauge Theory
We reformulate the Hamiltonian approach to lattice gauge theories such that,
at the classical level, the gauge group does not act canonically, but instead
as a Poisson-Lie group. At the quantum level, it then gets promoted to a
quantum group gauge symmetry. The theory depends on two parameters - the
deformation parameter and the lattice spacing . We show that the
system of Kogut and Susskind is recovered when , while
QCD is recovered in the continuum limit (for any ). We thus have the
possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil
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