Modeling cosmic ray anisotropies near 10(18) eV

A galactic magnetic field reversal near the Sagittarius spiral arm may be responsible for the southern excess (or northern shortage) of cosmic rays near 10 to the 18th power eV. The north-south asymmetry produced by such a reversal would increase with energy in the same manner as the observed asymmetry. The existence of a reversal has been inferred from analyses of Faraday rotation measures

Statistics of conductance and shot-noise power for chaotic cavities

We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$. With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ are calculated explicitly. We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges. For $0<g<1$ a power law for the conductance distribution is exact. All results are also consistent with numerical simulations.Comment: 7 pages, 3 figures. Proc. of the 3rd Workshop on Quantum Chaos and Localisation Phenomena, Warsaw, Poland, May 25-27, 200

Induced Ginibre ensemble of random matrices and quantum operations

A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.Comment: 2nd version, 34 pages, 5 figure

In Search of a Source for the 320 Eev Fly's Eye Cosmic Ray

The 320 EeV air shower detected by the Fly's Eye poses an important problem. Careful analysis of pathlength limitations for the possible particle types due to cosmic background radiation verifies that the particle very likely traveled less than 50 Mpc from its source. The best candidates for accelerating particles to such high energies are the very powerful radiogalaxies, however they are all more than 100 Mpc distant. Our search finds no likely source within 50 Mpc in the direction from which the particle arrived. This prompts consideration of less likely astrophysical sources, like M82, as well as non-standard mechanisms like cosmic string annihilation. It is also conceivable that the air shower was produced by some non-standard particle whose pathlength is unlimited because it does not interact with the cosmic background radiation. A less radical alternative is that relatively strong magnetic fields deflected the particle's path through a large angle, so it could have originated at a nearby radiogalaxy at an earlier time of strong activity.Comment: 27 pages, LaTeX, figures available by anonymous ftp, to appear in ApJ (3/1/95

Role of electron-electron and electron-phonon interaction effect in the optical conductivity of VO2

We have investigated the charge dynamics of VO2 by optical reflectivity measurements. Optical conductivity clearly shows a metal-insulator transition. In the metallic phase, a broad Drude-like structure is observed. On the other hand, in the insulating phase, a broad peak structure around 1.3 eV is observed. It is found that this broad structure observed in the insulating phase shows a temperature dependence. We attribute this to the electron-phonon interaction as in the photoemission spectra.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.

Random Bistochastic Matrices

Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.Comment: 22 pages, 4 figure

Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces \T={\rm Tr}(tt^\dag)^n, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables whose probability distribution depends on the symmetries of the system. For the case of broken time-reversal symmetry, we present explicit closed expressions for the average value and for the variance of \T for all $n$. In particular, this provides the charge cumulants \Q of all orders. We also compute the moments $$ of the conductance $g=\mathcal{T}_1$. All the results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of open channels.Comment: 5 pages, 4 figures. v2-minor change