C*-Algebras over Topological Spaces: Filtrated K-Theory

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe a space with four points and two C*-algebras over this space in the bootstrap class that have isomorphic filtrated K-theory but are not KK(X)-equivalent. For this particular space, we enrich filtrated K-theory by another K-theory functor, so that there is again a Universal Coefficient Theorem. Thus the enriched filtrated K-theory is a complete invariant for purely infinite, stable C*-algebras with this particular spectrum and belonging to the appropriate bootstrap class.Comment: Changes to theorem and equation numbering

Cutoff Effects on Energy-Momentum Tensor Correlators in Lattice Gauge Theory

We investigate the discretization errors affecting correlators of the energy-momentum tensor $T_{\mu\nu}$ at finite temperature in SU($N_c$) gauge theory with the Wilson action and two different discretizations of $T_{\mu\nu}$. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time $x_0$ and spatial momentum ${\bf p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^3x T_{00}$ has much larger discretization errors than the correlator of momentum $\int d^3x T_{0k}$. Secondly, the shear and diagonal stress correlators ($T_{12}$ and $T_{kk}$) require \Nt\geq 8 for the $Tx_0={1/2}$ point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with \as/\at=2 are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite ${\bf p}$ correlators.Comment: 16 pages, 5 figure

Late evolution of cataclysmic variables: the loss of AM Her systems

The white dwarf in AM Her systems is strongly magnetic and keeps in synchronous rotation with the orbit by magnetic coupling to the secondary star. As the latter evolves through mass loss to a cool, degenerate brown dwarf it can no longer sustain its own magnetic field and coupling is lost. Angular momentum accreted then spins up the white dwarf and the system no longer appears as an AM Her system. Possible consequences are run-away mass transfer and mass ejection from the system. Some of the unusual cataclysmic variable systems at low orbital periods may be the outcome of this evolution.Comment: 6 pages, 1 figure, Proceedings of "Cataclysmic Variables", Symposium in Honour of Brian Warner, Oxford 1999, eds. P.Charles, A.King, O'Donoghue, to appea

SU Uma stars: Rebrightenings after superoutburst

SU Uma stars after their long superoutbursts often show single or multiple rebrightenings. We show how this phenomenon can be understood as repeated reflections of transition waves which mediate changes between the hot and the cool state of the accretion disk and travel back and forth in the outer disk region, leaving an inner part permanently hot. This points to a temporarily increased viscosity, possibly related to the formation of large-scale and longer persisting magnetic fields by the dynamo operation during the long superoutburst. The 'mini-rebrightenings' in the early post-outburst light curve of V585 Lyr discovered by Kato and Osaki in Kepler observations seem to be understandable as a small limit cycle of low luminosity changes originating from a wiggle-feature in the thermal equilibrium curve of the cool optically thick disk.Comment: 9 pages, 6 figures, accepted for publication in PAS

Dynamical linke cluster expansions: Algorithmic aspects and applications

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline an associated multiple-line graph theory involving extended notions of connectivity and indicate an algorithmic implementation of graphs. Fields of applications are SU(N) gauge Higgs systems within variational estimates, spin glasses and partially annealed neural networks. We present results for the critical line in an SU(2) gauge Higgs model for the electroweak phase transition. The results agree well with corresponding high precision Monte Carlo results.Comment: LATTICE98(algorithms

A disk in the Galactic Center in the past ?

We raise the question whether in the past a disk could have existed in our Galactic Center which has disappeared now. Our model for the interaction of a cool disk and a hot corona above (Liu et al. 2004) allows to estimate an upper limit for the mass that might have been present in a putative accretion disk after a last star forming event, but would now have evaporated by coronal action.Comment: 2 pages, Contribution to Conference Proc. "Growing Black Holes", Garching, 2004, Eds. A. Merloni, S. Nayakshin, R. Sunyaev, Springer series "ESO Astrophysics Symposia", in prin