17,482 research outputs found
The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy
It is shown how the complex sine-Gordon equation arises as a symmetry flow of
the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry
flows forming the Borel loop algebra. The complex sine-Gordon and the vector
Nonlinear Schrodinger equations appear as lowest negative and second positive
flows within the extended hierarchy. This is fully analogous to the well-known
connection between the sine-Gordon and mKdV equations within the extended mKdV
hierarchy.
A general formalism for a Toda-like symmetry occupying the ``negative''
sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel
sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update
Supersymmetry for integrable hierarchies on loop superalgebras
The algebraic approach is employed to formulate N=2 supersymmetry
transformations in the context of integrable systems based on loop
superalgebras with homogeneous gradation. We
work with extended integrable hierarchies, which contain supersymmetric AKNS
and Lund-Regge sectors.
We derive the one-soliton solution for which solves positive and
negative evolution equations of the N=2 supersymmetric model.Comment: Latex, 21 page
The three-dimensional noncommutative Gross-Neveu model
This work is dedicated to the study of the noncommutative Gross-Neveu model.
As it is known, in the canonical Weyl-Moyal approach the model is inconsistent,
basically due to the separation of the amplitudes into planar and nonplanar
parts. We prove that if instead a coherent basis representation is used, the
model becomes renormalizable and free of the aforementioned difficulty. We also
show that, although the coherent states procedure breaks Lorentz symmetry in
odd dimensions, in the Gross-Neveu model this breaking can be kept under
control by assuming the noncommutativity parameters to be small enough. We also
make some remarks on some ordering prescriptions used in the literature.Comment: 10 pages, IOP article style; v3: revised version, accepted for
publication in J. Phys.
Cooperative localization-delocalization in the high Tc cuprates
The intrinsic metastable crystal structure of the cuprates results in local
dynamical lattice instabilities, strongly coupled to the density fluctuations
of the charge carriers. They acquire in this way simultaneously both,
delocalized and localized features. It is responsible for a partial fractioning
of the Fermi surface, i.e., the Fermi surface gets hidden in a region around
the anti-nodal points, because of the opening of a pseudogap in the normal
state, arising from a partial charge localization. The high energy localized
single-particle features are a result of a segregation of the homogeneous
crystal structure into checker-board local nano-size structures, which breaks
the local translational and rotational symmetry. The pairing in such a system
is dynamical rather than static, whereby charge carriers get momentarily
trapped into pairs in a deformable dynamically fluctuating ligand environment.
We conclude that the intrinsically heterogeneous structure of the cuprates must
play an important role in this type of superconductivity.Comment: 14 pages, 8 figures, Proceedings of the "International Conference on
Condensed Matter Theories", Quito, 2009 Int. J. Mod. Phys. B 2010 (Accepted
Tuning in magnetic modes in Tb(Co_{x}Ni_{1-x})_{2}B_{2}C: from longitudinal spin-density waves to simple ferromagnetism
Neutron diffraction and thermodynamics techniques were used to probe the
evolution of the magnetic properties of Tb(Co_{x}Ni_{1-x})_{2}B_{2}C. A
succession of magnetic modes was observed as x is varied: the longitudinal
modulated k=(0.55,0,0) state at x=0 is transformed into a collinear
k=([nicefrac]\nicefrac{1}{2},0,[nicefrac]\nicefrac{1}{2})
antiferromagnetic state at x= 0.2, 0.4; then into a transverse c-axis modulated
k=(0,0,[nicefrac]\nicefrac{1}{3}) mode at x= 0.6, and finally
into a simple ferromagnetic structure at x= 0.8 and 1. Concomitantly, the
low-temperature orthorhombic distortion of the tetragonal unit cell at x=0 is
reduced smoothly such that for x >= 0.4 only a tetragonal unit cell is
manifested. Though predicted theoretically earlier, this is the first
observation of the k=(0,0,[nicefrac]\nicefrac{1}{3}) mode in
borocarbides; our findings of a succession of magnetic modes upon increasing x
also find support from a recently proposed theoretical model. The implication
of these findings and their interpretation on the magnetic structure of the
RM_{2}B_{2}C series are also discussed
Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra
The construction of a q-deformed N=2 superconformal algebra is proposed in
terms of level 1 currents of quantum affine
Lie algebra and a single real Fermi field. In particular, it suggests the
expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its
constituents generate two isomorphic quadratic algebraic structures. The
generalization to is also proposed.Comment: AMSLATEX, 21page
Einstein gravity as a 3D conformally invariant theory
We give an alternative description of the physical content of general
relativity that does not require a Lorentz invariant spacetime. Instead, we
find that gravity admits a dual description in terms of a theory where local
size is irrelevant. The dual theory is invariant under foliation preserving
3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume
(for the spatially compact case). Locally, this symmetry is identical to that
of Horava-Lifshitz gravity in the high energy limit but our theory is
equivalent to Einstein gravity. Specifically, we find that the solutions of
general relativity, in a gauge where the spatial hypersurfaces have constant
mean extrinsic curvature, can be mapped to solutions of a particular gauge
fixing of the dual theory. Moreover, this duality is not accidental. We provide
a general geometric picture for our procedure that allows us to trade foliation
invariance for conformal invariance. The dual theory provides a new proposal
for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections
On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type
A deformation parameter of a bihamiltonian structure of hydrodynamic type is
shown to parameterize different extensions of the AKNS hierarchy to include
negative flows. This construction establishes a purely algebraic link between,
on the one hand, two realizations of the first negative flow of the AKNS model
and, on the other, two-component generalizations of Camassa-Holm and Dym type
equations.
The two-component generalizations of Camassa-Holm and Dym type equations can
be obtained from the negative order Hamiltonians constructed from the Lenard
relations recursively applied on the Casimir of the first Poisson bracket of
hydrodynamic type. The positive order Hamiltonians, which follow from Lenard
scheme applied on the Casimir of the second Poisson bracket of hydrodynamic
type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS
Hamiltonians give rise to charges conserved with respect to equations of motion
of two-component Camassa-Holm and two-component Dym type equations.Comment: 20 pages, Late
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