627 research outputs found
Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures
In this paper we examine the bi-Hamiltonian structure of the generalized
KdV-hierarchies. We verify that both Hamiltonian structures take the form of
Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated
system. Classical extended conformal algebras are obtained from the second
Poisson bracket. In particular, we construct the algebras, first
discussed for the case and by A. Polyakov and M. Bershadsky.Comment: 41 page
A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies
A family of mappings from the solution spaces of certain generalized
Drinfeld-Sokolov hierarchies to the self-dual Yang-Mills system on R^{2,2} is
described. This provides an extension of the well-known relationship between
self-dual connections and integrable hierarchies of AKNS and Drinfeld-Sokolov
type
Field-dependent Mossbauer relaxation study of domain walls in the quasi 1-d antiferromagnet RbFeCl3.2H2O
Quantum Matter and Optic
The experienced positive and negative influence of HIV on quality of life of people with HIV and vulnerable to HIV in the Netherlands
In Situ X-ray Absorption Spectroscopy of LaFeO<sub>3</sub> and LaFeO<sub>3</sub>/LaNiO<sub>3</sub> Thin Films in the Electrocatalytic Oxygen Evolution Reaction
We study the electrocatalytic oxygen evolution reaction using in situ X-ray absorption spectroscopy (XAS) to track the dynamics of the valence state and the covalence of the metal ions of LaFeO3 and LaFeO3/LaNiO3 thin films. The active materials are 8 unit cells grown epitaxially on 100 nm conductive La0.67Sr0.33MnO3 layers using pulsed laser deposition (PLD). The perovskite layers are supported on monolayer Ca2Nb3O10 nanosheet-buffered 100 nm SiNx membranes. The in situ Fe and Ni K-edges XAS spectra were measured from the backside of the SiNx membrane using fluorescence yield detection under electrocatalytic reaction conditions. The XAS spectra show significant spectral changes, which indicate that (1) the metal (co)valencies increase, and (2) the number of 3d electrons remains constant with applied potential. We find that the whole 8 unit cells react to the potential changes, including the buried LaNiO3 film.</p
Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
The matrix version of the -KdV hierarchy has been recently
treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian
symmetry reduction applied to a Poisson submanifold in the dual of the Lie
algebra . Here a
series of extensions of this matrix Gelfand-Dickey system is derived by means
of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra
using the natural
embedding for any positive integer. The
hierarchies obtained admit a description in terms of a matrix
pseudo-differential operator comprising an -KdV type positive part and a
non-trivial negative part. This system has been investigated previously in the
case as a constrained KP system. In this paper the previous results are
considerably extended and a systematic study is presented on the basis of the
Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson
brackets and makes clear the conformal (-algebra) structures related to
the KdV type hierarchies. Discrete reductions and modified versions of the
extended -KdV hierarchies are also discussed.Comment: 60 pages, plain TE
Susy Hierarchies and Affine Algebras
We review some basic features of the Lie-algebraic classification of
W-algebras and related integrable hierarchies in 1+1 dimensions, pointing out
the role of affine Lie algebras. We emphasize that the supersymmetric
extensions of the above construction possibly lead, though some questions are
still opened, to the classification of supersymmetric hierarchies based on
``generic'' supersymmetric affine Lie algebras. Here the word generic is used
to make clear that well-known procedures, as those introduced by Inami and
Kanno, are too restricted and do not lead to the full spectrum of
supersymmetric integrable hierarchies one can construct. A particular attention
is devoted to the large-N supersymmetric extensions (here N=4). The attention
paid by large-N theories being due to the fact that they arise as dimensional
reduction of N=1 models, and moreover that they realize an ``unification'' of
known hierarchies.Comment: 11 pages, LaTex, uses lamuphys.sty: talk given at the UIC
``Supersymmetry and Integrable Systems Workshop'', Chicago, June 12-14 199
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