K. A. Muttalib

Random matrix models with additional interactions

It has been argued that, despite remarkable success, existing random matrix theories are not adequate at describing disordered conductors in the metallic regime, due to the presence of certain two-body interactions in the effective Hamiltonian for the eigenvalues, in addition to the standard logarithmic interaction that arises entirely from symmetry considerations. We present a new method that allows exact solution of random matrix models with such additional two-body interactions. This should broaden the scope of random matrix models in general.

The determination of diffusion tensors in surface diffusion by the fluctuation method (theory)

Abstract An extension of the field emission fluctuation method for studying the diffusion of adsorbates on metal surfaces to the measurement of anisotropic diffusion is described. The modification consists of using a long, narrow rectangular slit as probed region. This allows a determination of the decay of the correlation function along the narrow direction only, so that, by rotating the slit to coincide with the principal axes of the diffusion tensor, its diagonal elements can be found. The determination of principal axes when these are fixed by substrate symmetry, and also when this symmetry is broken by adsorbate overlayers is discussed. Relevant equations for density and field emission current correlation functions are derived and numerically integrated where necessary. It is also shown that the mean square fluctuation for a slit can be orientation dependent and that such measurements can give information on correlation lengths in various directions.

New Class of Random Matrix Ensembles with Multifractal Eigenvectors

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three ensembles belong to a new class of critical RME with multifractal eigenfunction statistics and a universal critical spectral statitics. The generic form of the two-level correlation function for weak and extremely strong multifractality is suggested. Applications to the spectral statistics at the Anderson transition and for certain systems on the border of chaos and integrability is discussed.

Asymptotics of basic Bessel functions and q -Laguerre polynomials

Abstract We establish a large n complete asymptotic expansion for q -Laguerre polynomials and a complete asymptotic expansion for a q -Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907).

ONE-SIDED LOG-NORMAL DISTRIBUTION OF CONDUCTANCES FOR A DISORDERED QUANTUM WIRE

Since the discovery of the absence of self-averaging in mesoscopic disordered systems [1], the study of the full distribution of conductance has attracted a lot of attention [2]. In particular, while the metallic regime is well described by a Gaussian distribution, the moments of the conductance fluctuations become of the same order of magnitude as the average conductance on approaching the localized regime. In such cases the average value becomes insufficient in describing properties of disordered conductors and the full distribution must be considered. Recently, numerical support for the existence of a new universal distribution at the metal-insulator transition [3], a broad distribution of the critical conductance at the integer quantum Hall transition [4], as well as the expected multifractal properties associated with the critical regime [5], have increased the interest in the conductance distribution in the intermediate regime, between the wellstudied universal conductance fluctuations in the metallic limit and the log-normal distribution in the deeply insulating limit. However, even for a quasi-one-dimensional (1D) system where there is only a smooth crossover between the metallic and insulating regimes, there is no analytic result available for the conductance distribution in the crossover regime. So far only the first two moments have been obtained for all strengths of disorder [6], using the 1D supersymmetric nonlinear s model [7]. This model has been shown [8] to be equivalent, in the thick wire or quasi-1D limit, to the Dorokov-Mello-PereyraKumar (DMPK) equation [9] which describes the evolution of the distribution of the transmission eigenvalues with increasing wire length. In this work we develop a simple systematic method to evaluate directly the full distribution of conductance for a thick quasi-1D wire (mean free path l ? the width), starting from the solution of the DMPK equation. The main result of the paper is that although there is no phase transition in quasi-one-dimension, the crossover region between metallic and insulating regimes is highly nontrivial, and shows a remarkable “one-sided” log-normal distribution. Recent numerical studies of a quasi-1D system in the quantum Hall regime have shown highly asymmetric log-normal distributions in the crossover region [10]. We expect similar qualitative features to exist in the critical regimes in higher dimensions as well. Indeed, numerical studies near the integer quantum Hall transition in two dimensions as well as the Anderson transition in three dimensions also point to asymmetric distributions of the critical conductance [11]. In addition, we predict that even the insulating regime should have a sharp cutoff in its log-normal tail near the (dimensionless) conductance g 1. In particular, we show that the conductance distribution in the insulating regime (in the absence of time reversal symmetry) has the form

Weak-Localization Correction to the Anomalous Hall Effect in Polycrystalline Fe Films

In situ transport measurements have been made on ultrathin (<100 A thick) polycrystalline Fe films as a function of temperature and magnetic field for a wide range of disorder strengths. For sheet resistances Rxx less than approximately 3kOmega, we find a logarithmic temperature dependence of the anomalous Hall conductivity sigmaxy, which is shown for the first time to be due to a universal scale dependent weak-localization correction within the skew-scattering model. For higher sheet resistance, granularity becomes important and the break down of universal behavior becomes manifest as the prefactors of the lnT correction term to sigmaxx and sigmaxy decrease at different rates with increasing disorder.

Conductance distribution in disordered quantum wires: Crossover between the metallic and insulating regimes

We calculate the distribution of the conductance

Nonanalyticity in the distribution of conductances in quasi–one-dimensional wires

P(g)

GENERALIZED FOKKER-PLANCK EQUATION FOR MULTICHANNEL DISORDERED QUANTUM CONDUCTORS

for a quasi-one-dimensional system in the metal to insulator crossover regime, based on a recent analytical method valid for all strengths of disorder. We show the evolution of

Anomalous Hall effect in ferromagnetic disordered metals

P(g)