Broadening of a nonequilibrium phase transition by extended structural defects

We study the effects of quenched extended impurities on nonequilibrium phase transitions in the directed percolation universality class. We show that these impurities have a dramatic effect: they completely destroy the sharp phase transition by smearing. This is caused by rare strongly coupled spatial regions which can undergo the phase transition independently from the bulk system. We use extremal statistics to determine the stationary state as well as the dynamics in the tail of the smeared transition, and we illustrate the results by computer simulations.Comment: 4 pages, 4 eps figures, final version as publishe

Impact of embedding on predictability of failure-recovery dynamics in networks

Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component.We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. The loss of predictability due to these effects depend on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand predictability and controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in the global network.Comment: 22 pages, 20 figure

Bistability through triadic closure

We propose and analyse a class of evolving network models suitable for describing a dynamic topological structure. Applications include telecommunication, on-line social behaviour and information processing in neuroscience. We model the evolving network as a discrete time Markov chain, and study a very general framework where, conditioned on the current state, edges appear or disappear independently at the next timestep. We show how to exploit symmetries in the microscopic, localized rules in order to obtain conjugate classes of random graphs that simplify analysis and calibration of a model. Further, we develop a mean field theory for describing network evolution. For a simple but realistic scenario incorporating the triadic closure effect that has been empirically observed by social scientists (friends of friends tend to become friends), the mean field theory predicts bistable dynamics, and computational results confirm this prediction. We also discuss the calibration issue for a set of real cell phone data, and find support for a stratified model, where individuals are assigned to one of two distinct groups having different within-group and across-group dynamics

Gauge Field Theory Coherent States (GCS) : I. General Properties

In this article we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states $\psi_{(A,E)}$, labelled by a point (A,E) in the classical phase space, consisting of canonically conjugate pairs of connections A and electric fields E respectively, such that (a) they are eigenstates of a corresponding annihilation operator which is a generalization of A-iE smeared in a suitable way, (b) normal ordered polynomials of generalized annihilation and creation operators have the correct expectation value, (c) they saturate the Heisenberg uncertainty bound for the fluctuations of $\hat{A},\hat{E}$ and (d) they do not use any background structure for their definition, that is, they are diffeomorphism covariant. This is the first paper in a series of articles entitled ``Gauge Field Theory Coherent States (GCS)'' which aim at connecting non-perturbative quantum general relativity with the low energy physics of the standard model. In particular, coherent states enable us for the first time to take into account quantum metrics which are excited {\it everywhere} in an asymptotically flat spacetime manifold. The formalism introduced in this paper is immediately applicable also to lattice gauge theory in the presence of a (Minkowski) background structure on a possibly {\it infinite lattice}.Comment: 40 pages, LATEX, no figure

Looking for Effects of Topology in the Dirac Spectrum of Staggered Fermions

We classify SU(3) gauge field configurations in different topological sectors by the smearing technique. In each sector we compute the distribution of low lying eigenvalues of the staggered Dirac operator. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero. The smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are thus insensitive to gauge field topology. On the smeared configurations, $4\nu$ eigenvalues go to zero in agreement with the index theorem.Comment: Poster at Lattice99(topology), 3 page

Complexifier Coherent States for Quantum General Relativity

Recently, substantial amount of activity in Quantum General Relativity (QGR) has focussed on the semiclassical analysis of the theory. In this paper we want to comment on two such developments: 1) Polymer-like states for Maxwell theory and linearized gravity constructed by Varadarajan which use much of the Hilbert space machinery that has proved useful in QGR and 2) coherent states for QGR, based on the general complexifier method, with built-in semiclassical properties. We show the following: A) Varadarajan's states {\it are} complexifier coherent states. This unifies all states constructed so far under the general complexifier principle. B) Ashtekar and Lewandowski suggested a non-Abelean generalization of Varadarajan's states to QGR which, however, are no longer of the complexifier type. We construct a new class of non-Abelean complexifiers which come close to the one underlying Varadarajan's construction. C) Non-Abelean complexifiers close to Varadarajan's induce new types of Hilbert spaces which do not support the operator algebra of QGR. The analysis suggests that if one sticks to the present kinematical framework of QGR and if kinematical coherent states are at all useful, then normalizable, graph dependent states must be used which are produced by the complexifier method as well. D) Present proposals for states with mildened graph dependence, obtained by performing a graph average, do not approximate well coordinate dependent observables. However, graph dependent states, whether averaged or not, seem to be well suited for the semiclassical analysis of QGR with respect to coordinate independent operators.Comment: Latex, 54 p., no figure

Localization transition, Lifschitz tails and rare-region effects in network models

Effects of heterogeneity in the suspected-infected-susceptible model on networks are investigated using quenched mean-field theory. The emergence of localization is described by the distributions of the inverse participation ratio and compared with the rare-region effects appearing in simulations and in the Lifschitz tails. The latter, in the linear approximation, is related to the spectral density of the Laplacian matrix and to the time dependent order parameter. I show that these approximations indicate correctly Griffiths Phases both on regular one-dimensional lattices and on small world networks exhibiting purely topological disorder. I discuss the localization transition that occurs on scale-free networks at $\gamma=3$ degree exponent.Comment: 9 pages, 9 figures, accepted version in PR

On (Cosmological) Singularity Avoidance in Loop Quantum Gravity

Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical General Relativity to spatially homogeneous situations which is then quantized by the methods of LQG. Thus, LQC is a quantum mechanical toy model (finite number of degrees of freedom) for LQG(a genuine QFT with an infinite number of degrees of freedom) which provides important consistency checks. However, it is a non trivial question whether the predictions of LQC are robust after switching on the inhomogeneous fluctuations present in full LQG. Two of the most spectacular findings of LQC are that 1. the inverse scale factor is bounded from above on zero volume eigenstates which hints at the avoidance of the local curvature singularity and 2. that the Quantum Einstein Equations are non -- singular which hints at the avoidance of the global initial singularity. We display the result of a calculation for LQG which proves that the (analogon of the) inverse scale factor, while densely defined, is {\it not} bounded from above on zero volume eigenstates. Thus, in full LQG, if curvature singularity avoidance is realized, then not in this simple way. In fact, it turns out that the boundedness of the inverse scale factor is neither necessary nor sufficient for curvature singularity avoidance and that non -- singular evolution equations are neither necessary nor sufficient for initial singularity avoidance because none of these criteria are formulated in terms of observable quantities.After outlining what would be required, we present the results of a calculation for LQG which could be a first indication that our criteria at least for curvature singularity avoidance are satisfied in LQG.Comment: 34 pages, 16 figure

Background Independent Quantum Gravity: A Status Report

The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the article should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the article is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the article to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ