Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double

We present the Drinfel'd realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary Serre relations. The construction of its quantum double is carried out. This allows us to give the universal R-matrix of DY(osp(1|2)).Comment: Latex2e, 21 page

On Casimir's Ghost

We define on the universal enveloping superalgebra of osp(1|2n) a nonstandard adjoint action, endowing it with a module structure. This allows, in particular, to construct a bosonic operator which anticommutes with all the fermionic generators and which appears to be the square root of a certain Casimir operator.Comment: LaTeX2e, 13 pages,also available at http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP587.ps.gz ; one sentence removed and a note added. Not a major revisio

Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians

We examine the two parameter deformed superalgebra $U_{qs}(sl(1|2))$ and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre presentation and in the $R$-matrix scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists an infinite number of Casimir operators, indexed by integers $p > 1$ in the undeformed case and by $p \in Z$ in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of functions on $SL_{qs}(1|2)$ is also given and higher tensor product representations are discussed. Finally, we construct quantum chain Hamiltonians based on the Casimir operators. In the deformed case we find two Hamiltonians which describe deformed $t-J$ models.Comment: 27 pages, LaTeX, one reference moved and one formula adde

On the Quasi-Hopf structure of deformed double Yangians

We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.Comment: 11 page

Remote Data Acquisition for SPS 352 MHz Superconducting Cavities

The SPS Machine is equipped with four SuperConducting (SC) Cavities. These are used to accelerate the beams during the electron and positron cycles of LEP. During the last two years the control system for these cavities has been upgraded to the LEP standard environment but, as the diagnostic capabilities were not sufficient to ensure their reliable operation, it was decided to build a Data Acquisition system based on commercial products. The present system is based on National Instrument PXI (an extension to CompactPCI for instrumentation) with 166 MHz Pentium running Windows NT and Labview5.1. In order to meet the user requirements, in terms of portability and speed, a client/server approach has been used. The Server can acquire 16 signals at a rate of 1 ms during the whole SPS supercycle. The Client is composed of a virtual oscilloscope interface (one or four channels) with on-line signal and timing selections and automatic data and user setting storage capabilities. The Client can run on the two platforms used at CERN (PC and HP/UX)

Control of total voltage in the large distributed RF system of LEP

The LEP RF system is made up of a large number of independent RF units situated around the ring near the interaction points. These have different available RF voltages depending on their type and they may be inactive or unable to provide full voltage for certain periods. The original RF voltage control system was based on local RF unit voltage function generators pre-loaded with individual tables for energy ramping. This was replaced this year by a more flexible global RF voltage control system. A central controller in the main control room has direct access to the units over the LEP TDM system via multiplexers and local serial links. It continuously checks the state of all the units and adjusts their voltages to maintain the desired total voltage under all conditions. This voltage is distributed among the individual units to reduce the adverse effects of RF voltage asymmetry around the machine as far as possible. The central controller is a VME system with 68040 CPU and real time multitasking operating system. Event driven communication handlers allow fast reliable concurrent data communication with the remote units. The RF unit low level RF G64 equipment controllers use a VME 68030 CPU to achieve the necessary response time and reliability

Noise and dissipation on coadjoint orbits

We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random attractors are found for this general class of systems when the Lie algebra is semi- simple, provided the top Lyapunov exponent is positive. We study two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown

Integrable XYZ Model with Staggered Anisotropy Parameter

We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.Comment: 8 pages ; epic packag

Deformed Double Yangian Structures

Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N)) are defined for any N, extending the previously known case of N=2. They realise deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras A_qp(sl(N)), these algebras contain subalgebras at critical values of the central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations are derived for their abstract generators.Comment: 16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarra

On sl(N) and sl(M|N) integrable open spin chains

We study open spin chains based on rational sl(N) and sl(M|N) R-matrices. We classify the solutions of the reflection equations, for both the soliton-preserving and soliton-non-preserving cases. We then write the Bethe equations for these open spin chains.Comment: Talk given by DA at SYMPHYS11, Prague, June 200