Anderson Localization in Disordered Vibrating Rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.Comment: 10 pages, 6 figure

Contribution of exclusive (π0π0,π0η,ηη)γ(\pi^0\pi^0, \pi^0\eta, \eta\eta)\gamma channels to the leading order HVP of the muon g−2g-2

We evaluate the contributions of $(\pi^0\pi^0, \pi^0\eta, \eta\eta)\gamma$ exclusive channels to the dispersion integral of the leading order HVP of the muon anomalous magnetic moment. These channels are included in some way in previous evaluations of the $\pi^0\omega, \eta\omega$ and $\eta\phi$ contributions to $a_{\mu}^{\rm had, LO}$, where the vector resonances (decaying into $\pi^0/\eta+ \gamma$) are assumed to be on-shell. Since the separation of resonance and background contributions in a given observable is, in general, a model-dependent procedure, here we use pseudoscalar mesons and the photon as the $in$ and $out$ states of the $e^+e^- \to (\pi^0\pi^0, \pi^0\eta, \eta\eta)\gamma$ $S$-matrix, such that the cross section contains the interferences among different contributing to the amplitudes. We find $a^{\rm had, LO}_{\mu}(P^0_1P^0_2\gamma)=(1.13\pm 0.13 ) \times 10^{-10}$, where uncertainties stem mainly from vector meson dominance model parameters. Improved experimental studies of these exclusive channels in the whole range below 2 GeV would reduce model-dependency

Exact relativistic models of thin disks around static black holes in a magnetic field

The exact superposition of a central static black hole with surrounding thin disk in presence of a magnetic field is investigated. We consider two models of disk, one of infinite extension based on a Kuzmin-Chazy-Curzon metric and other finite based on the first Morgan-Morgan disk. We also analyze a simple model of active galactic nuclei consisting of black hole, a Kuzmin-Chazy-Curzon disk and two rods representing jets, in presence of magnetic field. To explain the stability of the disks we consider the matter of the disk made of two pressureless streams of counterrotating charged particles (counterrotating model) moving along electrogeodesic. Using the Rayleigh criterion we derivate for circular orbits the stability conditions of the particles of the streams. The influence of the magnetic field on the matter properties of the disk and on its stability are also analyzed.Comment: 17 pages, 14 figures. arXiv admin note: text overlap with arXiv:gr-qc/0409109 by other author

Quantum Interference in Single Molecule Electronic Systems

We present a general analytical formula and an ab initio study of quantum interference in multi-branch molecules. Ab initio calculations are used to investigate quantum interference in a benzene-1,2-dithiolate (BDT) molecule sandwiched between gold electrodes and through oligoynes of various lengths. We show that when a point charge is located in the plane of a BDT molecule and its position varied, the electrical conductance exhibits a clear interference effect, whereas when the charge approaches a BDT molecule along a line normal to the plane of the molecule and passing through the centre of the phenyl ring, interference effects are negligible. In the case of olygoynes, quantum interference leads to the appearance of a critical energy $E_c$, at which the electron transmission coefficient $T(E)$ of chains with even or odd numbers of atoms is independent of length. To illustrate the underlying physics, we derive a general analytical formula for electron transport through multi-branch structures and demonstrate the versatility of the formula by comparing it with the above ab-initio simulations. We also employ the analytical formula to investigate the current inside the molecule and demonstrate that large counter currents can occur within a ring-like molecule such as BDT, when the point charge is located in the plane of the molecule. The formula can be used to describe quantum interference and Fano resonances in structures with branches containing arbitrary elastic scattering regions connected to nodal sites.Comment: 12 pages, 11 figure

Wannier-Stark ladders in one-dimensional elastic systems

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and viceversa.Comment: 10 pages, 6 figures, accepted in Phys. Rev. Let

SVtL: System Verification through Logic: tool support for verifying sliced hierarchical statecharts

SVtL is the core of a slicing-based verification environment for UML statechart models. We present an overview of the SVtL software architecture. Special attention is paid to the slicing approach. Slicing reduces the complexity of the verification approach, based on removing pieces of the model that are not of interest during verification. In [18] a slicing algorithm has been proposed for statecharts, but it was not able to handle orthogonal regions efficiently. We optimize this algorithm by removing false dependencies, relying on the broadcasting mechanism between different parts of the statechart model

Using late-time optical and near-infrared spectra to constrain Type Ia supernova explosion properties

The late-time spectra of Type Ia supernovae (SNe Ia) are powerful probes of the underlying physics of their explosions. We investigate the late-time optical and near-infrared spectra of seven SNe Ia obtained at the VLT with XShooter at $>$200 d after explosion. At these epochs, the inner Fe-rich ejecta can be studied. We use a line-fitting analysis to determine the relative line fluxes, velocity shifts, and line widths of prominent features contributing to the spectra ([Fe II], [Ni II], and [Co III]). By focussing on [Fe II] and [Ni II] emission lines in the ~7000-7500 \AA\ region of the spectrum, we find that the ratio of stable [Ni II] to mainly radioactively-produced [Fe II] for most SNe Ia in the sample is consistent with Chandrasekhar-mass delayed-detonation explosion models, as well as sub-Chandrasekhar mass explosions that have metallicity values above solar. The mean measured Ni/Fe abundance of our sample is consistent with the solar value. The more highly ionised [Co III] emission lines are found to be more centrally located in the ejecta and have broader lines than the [Fe II] and [Ni II] features. Our analysis also strengthens previous results that SNe Ia with higher Si II velocities at maximum light preferentially display blueshifted [Fe II] 7155 \AA\ lines at late times. Our combined results lead us to speculate that the majority of normal SN Ia explosions produce ejecta distributions that deviate significantly from spherical symmetry.Comment: 17 pages, 12 figure, accepted for publication in MNRA