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 $\cal W$-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 $\cal W$-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 $\cal W$-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.

Exciton Beats in GaAs Quantum Wells: Bosonic Representation and Collective Effects

We discuss light-heavy hole beats observed in transient optical experiments in GaAs quantum wells in terms of a free-boson coherent state model. This approach is compared with descriptions based on few-level representations. Results lead to an interpretation of the beats as due to classical electromagnetic interference. The boson picture correctly describes photon excitation of extended states and accounts for experiments involving coherent control of the exciton density and Rayleigh scattering beating.Comment: 4 pages, no figures. Accepted for publication in Solid State Communication

Commutator methods for unitary operators

We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Large families of locally smooth operators are also exhibited. Half of the paper is dedicated to applications, and a special emphasize is put on the study of cocycles over irrational rotations. It is apparently the first time that commutator methods are applied in the context of rotation algebras, for the study of their generators.Comment: 15 page

High–Speed Data Transmission Subsystem of the SEOSAR/PAZ Satellite

This paper analyzes a digital interface and bus system modeling and optimization of the SEOSAR/PAZ Earth Observation satellite. The important part of the satellite is an X–band Synthetic Aperture Radar instrument that integrates 384 Transmit/Receive Modules located in 12 antenna panels 7.5 m away from the central processor and controlled by a synchronous 10 Mbps bidirectional serial protocol. This type of mid–range point–to–multipoint transmission is affected by bit errors due to crosstalk, transmission line attenuation and impedance mismatches. The high–speed data communication network has been designed to optimize the transmission by using a simulation model of the data distribution system which takes into account the worst–case scenario and by developing a lab–scaled prototype which exhibits BER of 10-11 for an interfering signal of 10 Vpp. The result is a point–to–multipoint bidirectional transmission network optimized in both directions with optimal values of loads and equalization resistors. This high–speed data transmission subsystem provides a compact design through a simple solution

Nonleptonic B→D(∗)DsJ(∗)B \to D^{(*)}D_{sJ}^{(*)} decays and the nature of the orbitally excited charmed-strange mesons

The Belle Collaboration has recently reported a study of the decays $B \to D_{s1}(2536)^{+}\bar{D}^{(\ast)}$ and has given also estimates of relevant ratios between branching fractions of decays $B \to D^{(\ast)}D_{sJ}^{(\ast)}$ providing important information to check the structure of the $D_{s0}^{\ast}(2317)$, $D_{s1}(2460)$ and $D_{s1}(2536)$ mesons. The disagreement between experimental data and Heavy Quark Symmetry has been used as an indication that $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ mesons could have a more complex structure than the canonical $c\bar{s}$ one. We analyze these ratios within the framework of a constituent quark model, which allows us to incorporate the effects given by finite $c$-quark mass corrections. Our findings are that while the $D_{s1}(2460)$ meson could have a sizable non-$q\bar{q}$ component, the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2536)$ mesons seem to be well described by a pure $q\bar{q}$ structure.Comment: 13 pages, 1 figur