257 research outputs found
The Hamiltonian Structure of Soliton Equations and Deformed W-Algebras
The Poisson bracket algebra corresponding to the second Hamiltonian structure
of a large class of generalized KdV and mKdV integrable hierarchies is
carefully analysed. These algebras are known to have conformal properties, and
their relation to -algebras has been previously investigated in some
particular cases. The class of equations that is considered includes
practically all the generalizations of the Drinfel'd-Sokolov hierarchies
constructed in the literature. In particular, it has been recently shown that
it includes matrix generalizations of the Gelfand-Dickey and the constrained KP
hierarchies. Therefore, our results provide a unified description of the
relation between the Hamiltonian structure of soliton equations and -algebras, and it comprises almost all the results formerly obtained by other
authors. The main result of this paper is an explicit general equation showing
that the second Poisson bracket algebra is a deformation of the Dirac bracket
algebra corresponding to the -algebras obtained through Hamiltonian
reduction.Comment: 41 pages, plain TeX, no figures. New introduction and references
added. Version to be published in Annals of Physics (N.Y.
Semi-classical spectrum of the Homogeneous sine-Gordon theories
The semi-classical spectrum of the Homogeneous sine-Gordon theories
associated with an arbitrary compact simple Lie group G is obtained and shown
to be entirely given by solitons. These theories describe quantum integrable
massive perturbations of Gepner's G-parafermions whose classical
equations-of-motion are non-abelian affine Toda equations. One-soliton
solutions are constructed by embeddings of the SU(2) complex sine-Gordon
soliton in the regular SU(2) subgroups of G. The resulting spectrum exhibits
both stable and unstable particles, which is a peculiar feature shared with the
spectrum of monopoles and dyons in N=2 and N=4 supersymmetric gauge theories.Comment: 28 pages, plain TeX, no figure
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PPAR gamma pro12Ala polymorphism and type 2 diabetes: a study in a spanish cohort
Type 2 diabetes (T2D) is a disease whose occurrence is increasing prevalent in westernized civilizations and is responsible for the proliferation in the morbidity and total mortality of patients with cardiovascular diseases, worldwide. However, the complexity in the treatment and prevention of T2D arises from the intricacy of the many physical and biological factors involved in its etiology. Impaired pathways for insulin signaling have been implicated as one the many factors in the development of T2D Individual peroxisome proliferator-activated receptors (PPARs) have previously exhibited associations with alterations of lipid profiles, fat tissue and T2D and displayed complications derived from high levels of glucose. However, PPARgamma has not yet been associated with the development or developmental pathways of T2D. We performed an observational study a Spanish cohort in order to better understand the association between the SNP PPARgamma polymorphism Pro12Ala in our patients and the incidence of T2D and other cardiovascular complications. We study did not find a statistically significant relationship between the Pro12Ala and T2D development in our cohort, future observations will help us to know the association with vascular disease in patients with T2D
L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments
Many studies on animal and human movement patterns report the existence of
scaling laws and power-law distributions. Whereas a number of random walk
models have been proposed to explain observations, in many situations
individuals actually rely on mental maps to explore strongly heterogeneous
environments. In this work we study a model of a deterministic walker, visiting
sites randomly distributed on the plane and with varying weight or
attractiveness. At each step, the walker minimizes a function that depends on
the distance to the next unvisited target (cost) and on the weight of that
target (gain). If the target weight distribution is a power-law, , in some range of the exponent , the foraging medium induces
movements that are similar to L\'evy flights and are characterized by
non-trivial exponents. We explore variations of the choice rule in order to
test the robustness of the model and argue that the addition of noise has a
limited impact on the dynamics in strongly disordered media.Comment: 15 pages, 7 figures. One section adde
A New and Elementary CP^n Dyonic Magnon
We show that the dressing transformation method produces a new type of dyonic
CP^n magnon in terms of which all the other known solutions are either
composites or arise as special limits. In particular, this includes the
embedding of Dorey's dyonic magnon via an RP^3 subspace of CP^n. We also show
how to generate Dorey's dyonic magnon directly in the S^n sigma model via the
dressing method without resorting to the isomorphism with the SU(2) principle
chiral model when n=3. The new dyon is shown to be either a charged dyon or
topological kink of the related symmetric-space sine-Gordon theories associated
to CP^n and in this sense is a direct generalization of the soliton of the
complex sine-Gordon theory.Comment: 21 pages, JHEP3, typos correcte
Interface Motion and Pinning in Small World Networks
We show that the nonequilibrium dynamics of systems with many interacting
elements located on a small-world network can be much slower than on regular
networks. As an example, we study the phase ordering dynamics of the Ising
model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at
zero temperature. In one and two dimensions, small-world features produce
dynamically frozen configurations, disordered at large length scales, analogous
of random field models. This picture differs from the common knowledge
(supported by equilibrium results) that ferromagnetic short-cuts connections
favor order and uniformity. We briefly discuss some implications of these
results regarding the dynamics of social changes.Comment: 4 pages, 5 figures with minor corrections. To appear in Phys. Rev.
Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories
We construct the soliton solutions in the symmetric space sine-Gordon
theories. The latter are a series of integrable field theories in
1+1-dimensions which are associated to a symmetric space F/G, and are related
via the Pohlmeyer reduction to theories of strings moving on symmetric spaces.
We show that the solitons are kinks that carry an internal moduli space that
can be identified with a particular co-adjoint orbit of the unbroken subgroup H
of G. Classically the solitons come in a continuous spectrum which encompasses
the perturbative fluctuations of the theory as the kink charge becomes small.
We show that the solitons can be quantized by allowing the collective
coordinates to be time-dependent to yield a form of quantum mechanics on the
co-adjoint orbit. The quantum states correspond to symmetric tensor
representations of the symmetry group H and have the interpretation of a fuzzy
geometric version of the co-adjoint orbit. The quantized finite tower of
soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final
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