L\'evy Processes on Uq(g)U_q(g) as Infinitely Divisible Representations

L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how the processes themselves can be reconstructed from their generators and study several classical stochastic processes that can be associated to these processes.Comment: 13 pages, LATEX file, ASI-TPA/13/99 (TU Clausthal); 6/99 (Preprint-Reihe Mathmatik, Univ. Greifswald)

A universally programmable Quantum Cellular Automaton

We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton with external classical control into an autonomous one, thereby proving the computational equivalence of these two models. We use this technique to construct a universally programmable cellular automaton on a one-dimensional lattice with single cell dimension 12.Comment: 4 pages, 4 figures, minor changes in introduction, fixed typos, accepted for publication in Physical Review Letter

Implications of Constraints on Mass Parameters in the Higgs Sector of the Nonlinear Supersymmetric SU(5) Model

The Higgs sector of the minimal nonlinear supersymmetric SU(5) model contains three mass parameters. Although these mass parameters are essentially free at the electroweak scale, they might have particular values if they evolve from a particular constraints at the GUT scale through the RG equations. By assuming a number of simple constraints on these mass parameters at the GUT scale, we obtain their values at the electroweak scale through the RG equations in order to investigate the phenomenological implications. Some of them are found to be consistent with the present experimental data.Comment: 23 pages, 10 figure

Analytic determination of dynamical and mosaic length scales in a Kac glass model

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on

Patch-repetition correlation length in glassy systems

We obtain the patch-repetition entropy Sigma within the Random First Order Transition theory (RFOT) and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A l^{d-1} down to length-scales of the order of one, where A is a positive constant, s_c is the configurational entropy density and d the spatial dimension. In consequence, the only meaningful length that can be defined from patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical length-scales already discussed in the literature and show that it is always of the order of the largest static length. Our results provide new insights, which are particularly relevant for RFOT theory, on the possible real space structure of super-cooled liquids. They suggest that this structure differs from a mosaic of different patches having roughly the same size.Comment: 6 page

Basins of attraction of metastable states of the spherical pp-spin model

We study the basins of attraction of metastable states in the spherical $p$-spin spin glass model, starting the relaxation dynamics at a given distance from a thermalized condition. Weighting the initial condition with the Boltzmann distribution we find a finite size for the basins. On the contrary, a white weighting of the initial condition implies vanishing basins of attraction. We make the corresponding of our results with the ones of a recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps figure

Magnetic field induced charge and spin instabilities in cuprate superconductors

A d-wave superconductor, subject to strong phase fluctuations, is known to suffer an antiferromagnetic instability closely related to the chiral symmetry breaking in (2+1)-dimensional quantum electrodynamics (QED3). On the basis of this idea we formulate a "QED3 in a box" theory of local instabilities of a d-wave superconductor in the vicinity of a single pinned vortex undergoing quantum fluctuations around its equilibrium position. As a generic outcome we find an incommensurate 2D spin density wave forming in the neighborhood of a vortex with a concomitant "checkerboard" pattern in the local electronic density of states, in agreement with recent neutron scattering and tunneling spectroscopy measurements.Comment: 4 pages REVTeX + 2 PostScript figures included in text. Version to appear in PRL (minor stylistic changes, references updated). For related work and info visit http://www.physics.ubc.ca/~fran

X-ray Properties of the Abell 644 Cluster of Galaxies

We use new ASCA observations and archival ROSAT Position Sensitive Proportional Counter (PSPC) data to determine the X-ray spectral properties of the intracluster gas in Abell 644. From the overall spectrum, we determine the average gas temperature to be 8.64 (+0.67,-0.56) keV, and an abundance of 0.32 (+/-0.04) $Z_{\odot}$. The global ASCA and ROSAT spectra imply a cooling rate of 214 (+100,-91) $M_{\odot}$ yr$^{-1}$. The PSPC X-ray surface brightness profile and the ASCA data suggest a somewhat higher cooling rate. We determine the gravitational mass and gas mass as a function of radius. The total gravitating mass within 1.2 Mpc is $6.2\times10^{14}$ $M_{\odot}$, of which 20% is in the form of hot gas. There is a region of elevated temperature 1.5-5 arcmin to the west of the cluster center. The south-southwest region of the cluster also shows excess emission in the ROSAT PSPC X-ray image, aligned with the major axis of the optical cD galaxy in the center of the cluster. We argue that the cluster is undergoing or has recently undergone a minor merger. The combination of a fairly strong cooling flow and evidence for a merger make this cluster an interesting case to test the disruption of cooling flow in mergers.Comment: 26 pages LaTeX including 9 eps figures + 4 pages LaTeX tables (landscape); accepted to ApJ, uses aaspp