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We reconsider estimates for the heat kernel on weighted graphs recently found by Metzger and Stollmann. In the case that the weights satisfy a positive lower bound as well as a finite upper bound, we obtain a specialized lower estimate and a proper generalization of a previous upper estimate. Reviews: Math. Rev. 1979406, Zbl. Math. 0934.46042
We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium. PACS - Klassifikation: 03.65.Xp, 05.30.-d, 02.30. See the corresponding papers: Schmidt, Andreas U.: "Zeno Dynamics of von Neumann Algebras" and "Mathematics of the Quantum Zeno Effect" and the talk "Zeno Dynamics in Quantum Statistical Mechanics" - http://publikationen.ub.uni-frankfurt.de/volltexte/2005/1167/
The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. It is shown that the Zeno dynamics coincides with the modular dynamics of a localized subalgebra. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a variant of the Kato-Lie-Trotter product formula.
We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand-Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity. See the corresponding paper: Schmidt, Andreas U.: "Mathematical Problems of Gauge Quantum Field Theory: A Survey of the Schwinger Model" and the presentation "Infinite Infrared Regularization in Krein Spaces"
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge quantum field theory, I cover the following subjects: The axiomatics of quantum field theory, formulation of quantum field theory in terms of Wightman functions, reconstruction of the state space, the local formulation of gauge theories, indefiniteness of the Wightman functions in general and in the special case of the Schwinger model, the state space of the Schwinger model, special features of the model. New results are contained in the Mathematical Appendix, where I consider in an abstract setting the Pontrjagin space structure of a special class of indefinite inner product spaces - the so called quasi-positive ones. This is motivated by the indefinite inner product space structure appearing in the above context and generalizes results of Morchio and Strocchi [J. Math. Phys. 31 (1990) 1467], and Dubin and Tarski [J. Math. Phys. 7 (1966) 574]. See the corresponding paper: Schmidt, Andreas U.: "Infinite Infrared Regularization and a State Space for the Heisenberg Algebra" and the presentation "Infinite Infrared Regularization in Krein Spaces".
Der vorliegende Beitrag - die stark überarbeitete Fassung des Vortrages "Lektüren des Unausdeutbaren ", den der Verfasser im Januar 2004 im Rahmen der kulturwissenschaftlichen Vortragsreihe GrenzBereiche des Lesens hielt - ist auch erschienen in: literatur für leser 27 (2004), Heft 4, S. 181-199. Ein Beispiel für die Schwierigkeit der literarischen Lektüre gibt Friedrich Schmidt. Er untersucht Lektüremöglichkeiten für das formale wie semantische "Abgebrochensein" des literarischen Kunstwerks der Moderne, wie es in den Fragmenten Kafkas seinen exponierten Ausdruck findet. In diesen Texten tritt zur äußeren Unabgeschlossenheit des Textkorpus ein brüchiges Sinngefüge: die Endlosigkeit der Reflexionen und Handlungszüge, die Heterogenität der Erzählfiguren, die Inkonsistenz jeder Bedeutungskonstruktion von Seiten des Lesers. Indem überdies der Abbruch, als verlorene Schrift oder verschwiegene Botschaft, in Kafkas Fragmenten explizit zum Thema wird, erhebt sich der Text gleichzeitig zum metareflexiven Kommentar: er vollzieht selbst, wovon er spricht. Insofern handelt er – sprachskeptisch – vom Defizit seines eigenen Ausdrucks, das letztlich auch von Lektüren nie vollständig eingeholt werden kann.
We investigate transverse hadron spectra from relativistic nucleus-nucleus collisions which reflect important aspects of the dynamics - such as the generation of pressure - in the hot and dense zone formed in the early phase of the reaction. Our analysis is performed within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. Both transport models show their reliability for elementary pp as well as light-ion (C+C, Si+Si) reactions. However, for central Au+Au (Pb+Pb) collisions at bombarding energies above ~ 5 A.GeV the measured K+- transverse mass spectra have a larger inverse slope parameter than expected from the calculation. Thus the pressure generated by hadronic interactions in the transport models above ~ 5 A.GeV is lower than observed in the experimental data. This finding shows that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - is generated by strong partonic interactions in the early phase of central Au+Au (Pb+Pb) collisions.
We investigate hadron production as well as transverse hadron spectra in nucleus-nucleus collisions from 2 A.GeV to 21.3 A.TeV within two independent transport approaches (UrQMD and HSD) that are based on quark, diquark, string and hadronic degrees of freedom. The comparison to experimental data demonstrates that both approaches agree quite well with each other and with the experimental data on hadron production. The enhancement of pion production in central Au+Au (Pb+Pb) collisions relative to scaled pp collisions (the 'kink') is well described by both approaches without involving any phase transition. However, the maximum in the K+/Pi+ ratio at 20 to 30 A.GeV (the 'horn') is missed by ~ 40%. A comparison to the transverse mass spectra from pp and C+C (or Si+Si) reactions shows the reliability of the transport models for light systems. For central Au+Au (Pb+Pb) collisions at bombarding energies above ~ 5 A.GeV, however, the measured K +/- m-theta-spectra have a larger inverse slope parameter than expected from the calculations. The approximately constant slope of K+/-spectra at SPS (the 'step') is not reproduced either. Thus the pressure generated by hadronic interactions in the transport models above ~ 5 A.GeV is lower than observed in the experimental data. This finding suggests that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au+Au (Pb+Pb) collisions.
We investigate hadron production as well as transverse hadron spectra from proton-proton, proton-nucleus and nucleus-nucleus collisions from 2 A·GeV to 21.3 A·TeV within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. The comparison to experimental data on transverse mass spectra from pp, pA and C+C (or Si+Si) reactions shows the reliability of the transport models for light systems. For central Au+Au (Pb+Pb) collisions at bombarding energies above ~5 A·GeV, furthermore, the measured K± transverse mass spectra have a larger inverse slope parameter than expected from the default calculations. We investigate various scenarios to explore their potential effects on the K± spectra. In particular the initial state Cronin effect is found to play a substantial role at top SPS and RHIC energies. However, the maximum in the K+/..+ ratio at 20 to 30 A·GeV is missed by 40% and the approximately constant slope of the K± spectra at SPS energies is not reproduced either. Our systematic analysis suggests that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential µq and temperature T- should be generated by strong interactions in the early pre-hadronic/partonic phase of central Au+Au (Pb+Pb) collisions.
In this paper, I investigate more closely the contribution of modal operators to the semantics of comparatives and I show that there is no need for a maximality or minimality operator. Following Kratzer s (1981, 1991) analysis of modal elements, I assume that the meaning of a modal sentence is dependent on a conversational background and an ordering source. For comparative environments, I demonstrate that the ordering source reduces a set of possible degrees to a single degree that is most (or least) wanted or expected, i.e., maximality and minimality readings of comparative constructions are an effect of the pragmatic meaning of the modal.
Friedrich Hassaurek
(1885)
General August Willich
(1878)
in: Der Deutsche Kulturträger; Vol 1 (1913), p. 11-21; 64-65; 120-122; 267-271; 304-307; 458-466; 499-506; 506-512 41 S.
Die Fundmeldungen in Band 24 von Botanik und Naturschutz in Hessen tragen die laufenden Nummern 1750 bis 1872 und stammen von Rolf Angersbach, Kurt Baumann, Ralph Baumgärtel, Dieter Bickler, Dirk Bönsel, Wolfgang Ehmke, Christian Feuring, Thomas Gregor, Volker Holzgreve, Karsten Horn, Heinz Kalheber, Gerwin Kasperek, Matthias Kellner, Detlef Mahn, Hans Reichert, Bernd Sauerwein, Hjalmar Thiel, Bärbel Wellmann und Jochen Wulfhorst.