An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

The cotangent bundle $T^*X$ to a complex manifold $X$ is classically endowed with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where \cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X] as a subalgebra and an extra central parameter $t$. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If $P$ is any section of order zero of \W[T^*X], we show that \exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page

The damped harmonic oscillator in deformation quantization

We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schr\"{o}dinger picture by a star-product induced by a modified "Poisson bracket". We determine the eigenstates in the damped regime and compute the transition probability between states of the undamped harmonic oscillator after the system was submitted to dissipation.Comment: Plain LaTex file, 11 page

UPSS and G2

The Universal Propellant Servicing System (UPSS) is a dedicated mobile launcher propellant delivery method that will minimize danger and complexity in order to allow vehicles to be serviced and ultimately launched from a variety of locations previously not seen fit for space launch. The UPPS/G2 project is the development of a model, simulation, and ultimately a working application that will control and monitor the cryogenic fluid delivery to the rocket for testing purposes. To accomplish this, the project is using the programming language/environment Gensym G2. The environment is an all-inclusive application that allows development, testing, modeling, and finally operation of the unique application through graphical and programmatic methods. We have learned G2 through classes and trial-and-error, and are now in the process of building the application that will soon be able to be tested on apparatuses here at Kennedy Space Center, and eventually on the actual unit. The UPSS will bring near-autonomous control of launches to those that need it, as well it will be a great addition to NASA and KSC's operational viability and the opportunity to bring space launches to parts of the world, and in time constraints, once not thought possible

Methodology for Detecting Trace Amounts of Microchimeric DNA from Peripheral Murine White Blood Cells by Real-Time PCR

Real-time PCR methodology can successfully quantitate microchimeric cell populations at a concentration of 100 microchimeric cells/100,000 host cells; however, it has not been successful in quantitating DNA from trace numbers of microchimeric white blood cells which we reported are present in murine peripheral blood at a concentration as low as 2/100,000 host cells. We report methodology using primers for a portion of the H2-k(b) murine histocompatibility sequence, specific for the C57BL/6J mouse. When these primers were used in the presence of 11,000 μM primer, a 20-fold increase in the median manufacturer’s recommended concentration, the assay could be optimized to detect 34 pg of C57BL/6J DNA in a background of 2.5 μg of carrier BALB/cJ DNA (1/100,000). These conditions resulted in a detection limit half as sensitive as that found when no carrier DNA was present

New bases for a general definition for the moving preferred basis

One of the challenges of the Environment-Induced Decoherence (EID) approach is to provide a simple general definition of the moving pointer basis or moving preferred basis. In this letter we prove that the study of the poles that produce the decaying modes in non-unitary evolution, could yield a general definition of the relaxation, the decoherence times, and the moving preferred basis. These probably are the most important concepts in the theory of decoherence, one of the most relevant chapters of theoretical (and also practical) quantum mechanics. As an example we solved the Omnes (or Lee-Friedrich) model using our theory.Comment: 6 page

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

Volume preserving multidimensional integrable systems and Nambu--Poisson geometry

In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu--Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. All these dispersionless KP and dToda type equations can be studied via twistor geometry, by using the method of Gindikin's pencil of two forms. Following this approach we study the twistor construction of our volume preserving systems

On Two Theorems About Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl algebra W and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP(2n)), and as an application, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg, which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones).Comment: corrected typo

Closedness of star products and cohomologies

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.Comment: 16 page