7,502 research outputs found
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
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
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
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
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
A trick for passing degenerate points in Ashtekar formulation
We examine one of the advantages of Ashtekar's formulation of general
relativity: a tractability of degenerate points from the point of view of
following the dynamics of classical spacetime. Assuming that all dynamical
variables are finite, we conclude that an essential trick for such a continuous
evolution is in complexifying variables. In order to restrict the complex
region locally, we propose some `reality recovering' conditions on spacetime.
Using a degenerate solution derived by pull-back technique, and integrating the
dynamical equations numerically, we show that this idea works in an actual
dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style
file are include
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
Constructing entanglement witnesses for infinite-dimensional systems
It is shown that, every entangled state in an infinite-dimensional composite
system has a simple entanglement witness of the form with
a nonnegative number and a finite rank self-adjoint operator. We also
provide two methods of constructing entanglement witness and apply them to
obtain some entangled states that cannot be detected by the PPT criterion and
the realignment criterion.Comment: 15 page
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
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