Transmission eigenvalues and the bare conductance in the crossover to Anderson localization

We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance, g, and the individual eigenvalues $\tau_n$ of the transmission matrix $tt^\dagger$ whose sum equals g. In diffusive samples, the highest eigenvalue, $\tau_1$, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of $\tau_1$, is nearly equal to g. We find that the spacing between average values of $\ln\tau_n$ is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.Comment: 5 pages, 5 figure

Multi-Instanton Effects in QCD Sum Rules for the Pion

Multi-instanton contributions to QCD sum rules for the pion are investigated within a framework which models the QCD vacuum as an instanton liquid. It is shown that in singular gauge the sum of planar diagrams in leading order of the $1/N_{c}$ expansion provides similar results as the effective single-instanton contribution. These effects are also analysed in regular gauge. Our findings confirm that at large distances the correlator functions are more adequately described in the singular gauge rather than in the regular one.Comment: 11 pages RevTeX is use

Performance of the CMS Pixel Detector at an upgraded LHC

The CMS experiment will include a pixel detector for pattern recognition and vertexing. It will consist of three barrel layers and two endcaps on each side, providing three space-points up to a pseudoraditity of 2.1. Taking into account the expected limitations of its performance in the LHC environment an 8-9 layer pixel detector for an upgraded LHC is discussed.Comment: Contribution to the 10th European Symposium on Semiconductor Detectors, June 12 - 16, 2005 in Wildbad Kreuth, Germany. 6 pages, 4 figures, 1 table. Referee's comments implemente

Ballistic transport in disordered graphene

An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.Comment: 23 pages, 10 figure

Fluence Dependence of Charge Collection of irradiated Pixel Sensors

The barrel region of the CMS pixel detector will be equipped with ``n-in-n'' type silicon sensors. They are processed on DOFZ material, use the moderated p-spray technique and feature a bias grid. The latter leads to a small fraction of the pixel area to be less sensitive to particles. In order to quantify this inefficiency prototype pixel sensors irradiated to particle fluences between $4.7\times 10^{13}$ and 2.6\times 10^{15} \Neq have been bump bonded to un-irradiated readout chips and tested using high energy pions at the H2 beam line of the CERN SPS. The readout chip allows a non zero suppressed analogue readout and is therefore well suited to measure the charge collection properties of the sensors. In this paper we discuss the fluence dependence of the collected signal and the particle detection efficiency. Further the position dependence of the efficiency is investigated.Comment: 11 Pages, Presented at the 5th Int. Conf. on Radiation Effects on Semiconductor Materials Detectors and Devices, October 10-13, 2004 in Florence, Italy, v3: more typos corrected, minor changes required by the refere

Localization length in Dorokhov's microscopic model of multichannel wires

We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L^{-1}_c=N.\xi^{-1}$ for the considered systems with $N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disorder. The inverse localization length is defined from the exponential decay of the two-probe Landauer conductance, which is determined from an earlier transfer matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact expressions above differ qualitatively from Dorokhov's localization length identified as the length scaling parameter in his scaling description of the distribution of the participation ratio. For N=3 we also discuss the case where the coupled chains are arranged on a strip rather than periodically on a tube. From the transfer matrix treatment we also obtain reflection coefficients matrices which allow us to find mean free paths and to discuss their relation to localization lengths in the two- and three channel systems

Analytical Results for Random Band Matrices with Preferential Basis

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a random band matrix with a strongly fluctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of random band matrices with preferential basis. Our analytical results are in good agreement with (but more general than) recent numerical findings by Jacquod and Shepelyansky.Comment: 8 pages RevTex and 1 Figure, both uuencode

Localization in disordered superconducting wires with broken spin-rotation symmetry

Localization and delocalization of non-interacting quasiparticle states in a superconducting wire are reconsidered, for the cases in which spin-rotation symmetry is absent, and time-reversal symmetry is either broken or unbroken; these are referred to as symmetry classes BD and DIII, respectively. We show that, if a continuum limit is taken to obtain a Fokker-Planck (FP) equation for the transfer matrix, as in some previous work, then when there are more than two scattering channels, all terms that break a certain symmetry are lost. It was already known that the resulting FP equation exhibits critical behavior. The additional symmetry is not required by the definition of the symmetry classes; terms that break it arise from non-Gaussian probability distributions, and may be kept in a generalized FP equation. We show that they lead to localization in a long wire. When the wire has more than two scattering channels, these terms are irrelevant at the short distance (diffusive or ballistic) fixed point, but as they are relevant at the long-distance critical fixed point, they are termed dangerously irrelevant. We confirm the results in a supersymmetry approach for class BD, where the additional terms correspond to jumps between the two components of the sigma model target space. We consider the effect of random $\pi$ fluxes, which prevent the system localizing. We show that in one dimension the transitions in these two symmetry classes, and also those in the three chiral symmetry classes, all lie in the same universality class

How the recent BABAR data for P to \gamma\gamma* affect the Standard Model predictions for the rare decays P to l+l-

Measuring the lepton anomalous magnetic moments $(g-2)$ and the rare decays of light pseudoscalar mesons into lepton pairs $P\to l^{+}l^{-}$, serve as important tests of the Standard Model. To reduce the theoretical uncertainty in the standard model predictions, the data on the charge and transition form factors of the light pseudoscalar mesons play a significant role. Recently, new data on the behavior of the transition form factors $P\to\gamma\gamma*$ at large momentum transfer were supplied by the BABAR collaboration. There are several problems with the theoretical interpretation of these data: 1) An unexpectedly slow decrease of the pion transition form factor at high momenta, 2) the qualitative difference in the behavior of the pion form factor and the $\eta$ and $\eta^\prime$ form factors at high momenta, 3) the inconsistency of the measured ratio of the $\eta$ and $\eta^\prime$ form factors with the predicted one. We comment on the influence of the new BABAR data on the rare decay branchings.Comment: 11 pages, 3 figure

Conductance of 1D quantum wires with anomalous electron-wavefunction localization

We study the statistics of the conductance $g$ through one-dimensional disordered systems where electron wavefunctions decay spatially as $|\psi| \sim \exp (-\lambda r^{\alpha})$ for $0 <\alpha <1$, $\lambda$ being a constant. In contrast to the conventional Anderson localization where $|\psi| \sim \exp (-\lambda r)$ and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized ($\alpha <1$) the full statistics of the conductance is determined by the average $$ and the power $\alpha$. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value $\alpha =1/2$. To test our theory for other values of $\alpha$, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references updated. Published in PRB, Phys. Rev. B 85, 235450 (2012