Random matrix theory for CPA: Generalization of Wegner's nn--orbital model

We introduce a generalization of Wegner's $n$-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green's functions and the conductivity exactly in the limit $n\to\infty$. Our solution solves the CPA-equation of the $(n=1)$-Anderson model for arbitrarily distributed disorder. We show how the Lloyd model is included in our model.Comment: 3 pages, Rev-Te

Dickens\u27 Interest in the Theatre

In this study I have not been concerned with Charles Dickens as the man, or humorist, or novelist; but I have confined my investigation to Charles Dickens\u27 interest in the theatre. I shall show how he tried to express his theatrical ambitions by acting, producing, and directing plays though he was really a novelist; and how his entire career was colored by his interest in these various aspects of the theatre

Seven-fluorochrome mouse M-FISH for high-resolution analysis of interchromosomal rearrangements

The mouse has evolved to be the primary mammalian genetic model organism. Important applications include the modeling of human cancer and cloning experiments. In both settings, a detailed analysis of the mouse genome is essential. Multicolor karyotyping technologies have emerged to be invaluable tools for the identification of mouse chromosomes and for the deciphering of complex rearrangements. With the increasing use of these multicolor technologies resolution limits are critical. However, the traditionally used probe sets, which employ 5 different fluorochromes, have significant limitations. Here, we introduce an improved labeling strategy. Using 7 fluorochromes we increased the sensitivity for the detection of small interchromosomal rearrangements (700 kb or less) to virtually 100%. Our approach should be important to unravel small interchromosomal rearrangements in mouse models for DNA repair defects and chromosomal instability. Copyright (C) 2003 S. Karger AG, Basel

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Semigroups of distributions with linear Jacobi parameters

We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter $t$ if and only if the measures come from the Meixner class. Moreover, we prove the parallel result, in a more explicit way, for the free convolution and the free Meixner class. We then construct the class of measures satisfying the same property for the two-state free convolution. This class of two-state free convolution semigroups has not been considered explicitly before. We show that it also has Meixner-type properties. Specifically, it contains the analogs of the normal, Poisson, and binomial distributions, has a Laha-Lukacs-type characterization, and is related to the $q=0$ case of quadratic harnesses.Comment: v3: the article is merged back together with arXiv:1003.4025. A significant revision following suggestions by the referee. 2 pdf figure

Temporally Resolved Intensity Contouring (TRIC) for characterization of the absolute spatio-temporal intensity distribution of a relativistic, femtosecond laser pulse

Today's high-power laser systems are capable of reaching photon intensities up to $10^{22}$ W/cm^2, generating plasmas when interacting with material. The high intensity and ultrashort laser pulse duration (fs) make direct observation of plasma dynamics a challenging task. In the field of laser-plasma physics and especially for the acceleration of ions, the spatio-temporal intensity distribution is one of the most critical aspects. We describe a novel method based on a single-shot (i.e. single laser pulse) chirped probing scheme, taking nine sequential frames at framerates up to THz. This technique, to which we refer as temporally resolved intensity contouring (TRIC) enables single-shot measurement of laser-plasma dynamics. Using TRIC, we demonstrate the reconstruction of the complete spatio-temporal intensity distribution of a high-power laser pulse in the focal plane at full pulse energy with sub picosecond resolution.Comment: Daniel Haffa, Jianhui Bin and Martin Speicher are corresponding author

Open Access in UCL: a new paradigm for London's Global University in research support

Open Access provides an opportunity for researchers to disseminate their research globally, but it comes with challenges. This article looks at the various ways in which UCL (University College London) has addressed those challenges, by investing in Open Access activities at the university

Lowering and raising operators for the free Meixner class of orthogonal polynomials

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.Comment: 26 pages, REVTeX, 10 ps figures; changed conten