Neighbours of Einstein's Equations: Connections and Curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe

Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation

Quantum correlations have fundamental and technological interest, and hence many measures have been introduced to quantify them. Some hierarchical orderings of these measures have been established, e.g., discord is bigger than entanglement, and we present a class of bipartite states, called premeasurement states, for which several of these hierarchies collapse to a single value. Because premeasurement states are the kind of states produced when a system interacts with a measurement device, the hierarchy collapse implies that the uncertainty of an observable is quantitatively connected to the quantum correlations (entanglement, discord, etc.) produced when that observable is measured. This fascinating connection between uncertainty and quantum correlations leads to a reinterpretation of entropic formulations of the uncertainty principle, so-called entropic uncertainty relations, including ones that allow for quantum memory. These relations can be thought of as lower-bounds on the entanglement created when incompatible observables are measured. Hence, we find that entanglement creation exhibits complementarity, a concept that should encourage exploration into "entanglement complementarity relations".Comment: 19 pages, 2 figures. Added Figure 1 and various remarks to improve clarity of presentatio

A study of separability criteria for mixed three-qubit states

We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne and Seevinck dealing with matrix elements are the strongest ones for different separability classes of this 2 parameter state. As a new result we determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl

The reality conditions for the new canonical variables of General Relativity

We examine the constraints and the reality conditions that have to be imposed in the canonical theory of 4--d gravity formulated in terms of Ashtekar variables. We find that the polynomial reality conditions are consistent with the constraints, and make the theory equivalent to Einstein's, as long as the inverse metric is not degenerate; when it is degenerate, reality conditions cannot be consistently imposed in general, and the theory describes complex general relativity.Comment: 11

Degenerate Sectors of the Ashtekar Gravity

This work completes the task of solving locally the Einstein-Ashtekar equations for degenerate data. The two remaining degenerate sectors of the classical 3+1 dimensional theory are considered. First, with all densitized triad vectors linearly dependent and second, with only two independent ones. It is shown how to solve the Einstein-Ashtekar equations completely by suitable gauge fixing and choice of coordinates. Remarkably, the Hamiltonian weakly Poisson commutes with the conditions defining the sectors. The summary of degenerate solutions is given in the Appendix.Comment: 19 pages, late

A Note on trapped Surfaces in the Vaidya Solution

The Vaidya solution describes the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole. There has been a question whether closed trapped surfaces can extend into the flat region (whereas closed outer trapped surfaces certainly can). For the special case of self-similar collapse we show that the answer is yes, if and only if the mass function rises fast enough.Comment: 14 pages, 4 figures; minor polish added to version

Causal structure and degenerate phase boundaries

Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersufaces, the conjecture that the "phase boundary" separating the degenerate space-time region from the non-degenerate one in Ashtekar's gravity is always null is proved under certain circumstances.Comment: 13 pages, Revte

Screening of organically based fungicides for apple scab (Venturia inaequalis) control and a histopathological study of the mode of action of a resistance inducer.

A range of possible substitutes for copper-based fungicides for control of apple scab (Venturia inaequalis) in organic growing were tested in laboratory and growth chamber experiments in the Danish project StopScab (2002-2004). Eighteen crude plant extracts, 19 commercial plant-based products and 6 miscellaneous compounds were tested for their ability to reduce scab symptoms on apple seedlings. Most of the compounds were also tested for their effect on conidium germination on glass slides. Fourteen of the crude plant extracts, 13 of the commercial plant products and 5 of the miscellaneous compounds showed promising control efficacies when used either preventively or curatively in the plant assay. A histopathological study was carried out on the mode of action of the resistance inducer, acibenzolar-S-methyl (ASM), which reduced scab severity and sporulation on apple seedlings in several plant assays when applied as preventive treatment. The effect of the inducer on key pre- and post-penetration events of V. inaequalis was studied and compared to these events in water-treated control leaves. The histopathological study showed that the inducer had its strongest effect on post-penetration events indicated by delayed infection and reduced stroma development. In addition, a small but significant inhibition of conidial germination and a stimulation of germ tube length were observed. This investigation provides new histopathological evidence for the mode of action of ASM against V. inaequalis and serves as a model for evaluation of the mechanisms by which the organically based fungicides reduce infection of V. inaequalis

Robustness of Highly Entangled Multi-Qubit States Under Decoherence

We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |GHZ> state.Comment: 16 pages, 3 figures. Changes in Sec.

Extreme value modelling of storm damage in Swedish forests

International audienceForests cover about 56% of the land area in Sweden and forest damage due to strong winds has been a recurring problem. In this paper we analyse recorded storm damage in Swedish forests for the years 1965?2007. During the period 48 individual storm events with a total damage of 164 Mm³ have been reported with the severe storm on 8 to 9 January 2005, as the worst with 70 Mm³ damaged forest. For the analysis, storm damage data has been normalised to account for the increase in total forest volume over the period. We show that, within the framework of statistical extreme value theory, a Poisson point process model can be used to describe these storm damage events. Damage data supports a heavy-tailed distribution with great variability in damage for the worst storm events. According to the model, and in view of available data, the return period for a storm with damage in size of the severe storm of January 2005 is approximately 80 years, i.e. a storm with damage of this magnitude will happen, on average, once every eighty years. To investigate a possible temporal trend, models with time-dependent parameters have been analysed but give no conclusive evidence of an increasing trend in the normalised storm damage data for the period. Using a non-parametric approach with a kernel based local-likelihood method gives the same result