Quantization and the Resolvent Algebra

We introduce a novel commutative C*-algebra of functions on a symplectic vector space admitting a complex structure, along with a strict deformation quantization that maps a dense subalgebra to the resolvent algebra introduced by Buchholz and Grundling \cite{BG2008}. The associated quantization map is a field-theoretical Weyl quantization compatible with the work of Binz, Honegger and Rieckers \cite{BHR}. We also define a Berezin-type quantization map on the whole C*-algebra, which continuously and bijectively maps it onto the resolvent algebra. This C*-algebra, generally defined on a real inner product space X, intimately depends on the finite dimensional subspaces of X. We thoroughly analyze the structure and applicability of this algebra in the finite dimensional case by giving a characterization of its elements and by computing its Gelfand spectrum

Hysteretic clustering in granular gas

Granular material is vibro-fluidized in N=2 and N=3 connected compartments, respectively. For sufficiently strong shaking the granular gas is equi-partitioned, but if the shaking intensity is lowered, the gas clusters in one compartment. The phase transition towards the clustered state is of 2nd order for N=2 and of 1st order for N=3. In particular, the latter is hysteretic. The experimental findings are accounted for within a dynamical model that exactly has the above properties

UMTV: a Single Chip TV Receiver for PDAs, PCs and Cell Phones

A zero-external-component TV receiver for portable platforms is realized in a mainstream 8GHz-f/sub t/ BiCMOS process. Die size is 5/spl times/5mm/sup 2/ and power dissipation is 50mA at 3V. The receiver includes a single tunable LNA (3mA) with less than 5dB NF from 40 to 900MHz. The programmable IF filters cover all analog and digital standards

The formation and evolution of very massive stars in dense stellar systems

The early evolution of dense stellar systems is governed by massive single star and binary evolution. Core collapse of dense massive star clusters can lead to the formation of very massive objects through stellar collisions ($M\geq$ 1000 \msun). Stellar wind mass loss determines the evolution and final fate of these objects, and decides upon whether they form black holes (with stellar or intermediate mass) or explode as pair instability supernovae, leaving no remnant. We present a computationaly inexpensive evolutionary scheme for very massive stars that can readily be implemented in an N-body code. Using our new N-body code 'Youngbody' which includes a detailed treatment of massive stars as well as this new scheme for very massive stars, we discuss the formation of intermediate mass and stellar mass black holes in young starburst regions. A more detailed account of these results can be found in Belkus et al. 2007.Comment: 2 pages, 2 figures. To appear in conference proceedings for IAUS246, 200

Systematic Density Expansion of the Lyapunov Exponents for a Two-dimensional Random Lorentz Gas

We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at low density. The positive Lyapunov exponent may be obtained either by a direct analysis of the dynamics, or by the use of kinetic theory methods. To leading orders in the density of scatterers it is of the form $A_{0}\tilde{n}\ln\tilde{n}+B_{0}\tilde{n}$, where $A_{0}$ and $B_{0}$ are known constants and $\tilde{n}$ is the number density of scatterers expressed in dimensionless units. In this paper, we find that through order $(\tilde{n}^{2})$, the positive Lyapunov exponent is of the form $A_{0}\tilde{n}\ln\tilde{n}+B_{0}\tilde{n}+A_{1}\tilde{n}^{2}\ln\tilde{n} +B_{1}\tilde{n}^{2}$. Explicit numerical values of the new constants $A_{1}$ and $B_{1}$ are obtained by means of a systematic analysis. This takes into account, up to $O(\tilde{n}^{2})$, the effects of {\it all\/} possible trajectories in two versions of the model; in one version overlapping scatterer configurations are allowed and in the other they are not.Comment: 12 pages, 9 figures, minor changes in this version, to appear in J. Stat. Phy

Largest Lyapunov Exponent for Many Particle Systems at Low Densities

The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.Comment: 4 pages, RevTeX, 2 Figures (encapsulated postscript). Submitted to Phys. Rev. Let