Covariant Canonical Gauge theory of Gravitation resolves the Cosmological Constant Problem

The covariant canonical transformation theory applied to the relativistic theory of classical matter fields in dynamic space-time yields a new (first order) gauge field theory of gravitation. The emerging field equations embrace a quadratic Riemann curvature term added to Einstein's linear equation. The quadratic term facilitates a momentum field which generates a dynamic response of space-time to its deformations relative to de Sitter geometry, and adds a term proportional to the Planck mass squared to the cosmological constant. The proportionality factor is given by a dimensionless parameter governing the strength of the quadratic term. In consequence, Dark Energy emerges as a balanced mix of three contributions, (A)dS curvature plus the residual vacuum energy of space-time and matter. The Cosmological Constant Problem of the Einstein-Hilbert theory is resolved as the curvature contribution relieves the rigid relation between the cosmological constant and the vacuum energy density of matter

Canonical Transformation Path to Gauge Theories of Gravity

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the free gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of General Relativity.Comment: 16 page

Preheating after N-flation

We study preheating in N-flation, assuming the Mar\v{c}enko-Pastur mass distribution, equal energy initial conditions at the beginning of inflation and equal axion-matter couplings, where matter is taken to be a single, massless bosonic field. By numerical analysis we find that preheating via parametric resonance is suppressed, indicating that the old theory of perturbative preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity parameters and the scalar spectral index computed for N-flation are similar to those in single field inflation (at least within an observationally viable parameter region), our results suggest that the physics of preheating can differ significantly from the single field case.Comment: 14 pages, 14 figures, references added, fixed typo

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Wegner estimate for discrete alloy-type models

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10

Nanoscopic tip sensors fabricated by gas phase etching of optical glass fibers

Silica-based fiber tips are used in a variety of spectroscopic, micro- or nano-scopic optical sensor applications and photonic micro-devices. The miniaturization of optical sensor systems and the technical implementation using optical fibers can provide new sensor designs with improved properties and functionality for new applications. The selective-etching of specifically doped silica fibers is a promising method in order to form complex photonic micro structures at the end or within fibers such as tips and cavities in various shapes useful for the all-fiber sensor and imaging applications. In the present study, we investigated the preparation of geometrically predefined, nanoscaled fiber tips by taking advantage of the dopant concentration profiles of highly doped step-index fibers. For this purpose, a gas phase etching process using hydrofluoric acid (HF) vapor was applied. The shaping of the fiber tips was based on very different etching rates as a result of the doping characteristics of specific optical fibers. Technological studies on the influence of the etching gas atmosphere on the temporal tip shaping and the final geometry were performed using undoped and doped silica fibers. The influence of the doping characteristics was investigated in phosphorus-, germanium-, fluorine- and boron-doped glass fibers. Narrow exposed as well as protected internal fiber tips in various shapes and tip radiuses down to less than 15 nm were achieved and characterized geometrically and topologically. For investigations into surface plasmon resonance effects, the fiber tips were coated with nanometer-sized silver layers by means of vapour deposition and finally subjected to an annealing treatment

Ink dating using thermal desorption and gas chromatography / mass spectrometry: comparison of results obtained in two laboratories

Recent ink dating methods focused mainly on changes in solvent amounts occurring over time. A promising method was developed at the Landeskriminalamt of Munich using thermal desorption (TD) followed by gas chromatography / mass spectrometry (GC/MS) analysis. Sequential extractions of the phenoxyethanol present in ballpoint pen ink entries were carried out at two different temperatures. This method is applied in forensic practice and is currently implemented in several laboratories participating to the InCID group (International Collaboration on Ink Dating). However, harmonization of the method between the laboratories proved to be a particularly sensitive and time consuming task. The main aim of this work was therefore to implement the TD-GC/MS method at the Bundeskriminalamt (Wiesbaden, Germany) in order to evaluate if results were comparable to those obtained in Munich. At first validation criteria such as limits of reliable measurements, linearity and repeatability were determined. Samples were prepared in three different laboratories using the same inks and analyzed using two TDS-GC/MS instruments (one in Munich and one in Wiesbaden). The inter- and intra-laboratory variability of the ageing parameter was determined and ageing curves were compared. While inks stored in similar conditions yielded comparable ageing curves, it was observed that significantly different storage conditions had an influence on the resulting ageing curves. Finally, interpretation models, such as thresholds and trend tests, were evaluated and discussed in view of the obtained results. Trend tests were considered more suitable than threshold models. As both approaches showed limitations, an alternative model, based on the slopes of the ageing curves, was also proposed

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471