Periodic-orbit theory of level correlations

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.     

Numerical studies on the anderson localization problem

Our study of Anderson's tight binding model for strongly disordered electronic systems is extended to a numerical treatment of thed c-conductivity atT=0. For 100 × 100 square lattices, 129 × 129 triangular lattices, and for diamond lattices with 27,000 sites, the behaviour of is studied as a function of the Fermi energy and the disorder. The calculations are based on the exact eigenfunction representation of the Kubo formula, which is evaluated by the systematic application of recursion algorithms. Our results are in favour of Mott's original suggestion of a minimum metallic conductivity _min, both in two and three dimensions. In two dimensions we find the universal value of _min=(0.11 ±0.02)e ²/. Based on the thesis of J. Stein, Regensburg 1979     

Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

Diagrammatic theory for periodic anderson model

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of f — localized electrons as a main parameter of the theory. f-Electrons are strongly correlated and c-conduction electrons are uncorrelated. Correlation function for f- and mass operator for c-electrons are determined. The Dyson equation for c- and Dyson-type equation for f-electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential with respect to, the variation of the mass operator is established. The result is appropriate both for the normal and for the superconducting states of the system.     

Nonuniversality of anderson localization in short-range correlated disorder

We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief, we demonstrate that already next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single-parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results of numerical simulations are in full agreement with our theory, with no adjustable parameters.     

类Opal光子晶体红外区安德森定域化理论研究

本文根据Mie散射理论和低浓度近似下,对在中红外区高折射率半导体材料AlP等做为散射体的类Opal光子晶体的安德森定域化进行了理论研究,发现在浓度为10%,折射率比值大于3.8,无吸收状态下,此类晶体将出现两个定域化区.同时为此类晶体的定域化研究提供了一个比较理想的处理方法.     

Systematic treatment of the anderson localization on the basis of the projection operator formalism

A derivation within the projection operator technique is given for the density and current response functions of a system of independent particles moving in a random potential. The essential point is the derivation of kinetic equations for the current relaxation kernel instead of for the density propagator as in a previous treatment on the basis of the projection operator formalism. In these equations the divergent contributions from the 2k _F -scattering mechanism can be systematically separated from those of diffusional scattering. Especially, both the self-consistent current relaxation theory, developed by Götze and the self-consistent treatment of Vollhardt and Wölfle are rederived from simple approximations of the kinetic equations. The outlined method represents a systematic approach to the Anderson localization. It may be applicable also to more realistic models for the Anderson localization as well as extended to the evaluation of general transport coefficients on a level far beyond the usual perturbation theories.     

Self-consistent perturbation theory of the anderson model: Ground state properties

The zero temperature limit of the self-consistent perturbation theory of a degenerate Anderson impurityin a metal is partially solved with analytical methods. In particular, the energy scales relevant to the system are made explicit and closed expressions are derived for the local level propagator around the Fermi energy and for the dynamical susceptibility. Results are compared with what is known from Fermi liquid theory. The argument that the theory is valid for large degeneracy is disturbed by certain pathologies.Supported by DFG through the research program of Sonderforschungsbereich 125 (Aachen-Jülich-Köln)     

Scaling in the one-dimensional anderson localization problem in the region of fluctuation states

We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not valid, the distribution can still be described within a scaling approach based upon the ratio of two fundamental quantities, the localization length, l(loc), and a new length, l(s), related to the integral density of states. In an intermediate interval of the system's length L, l(loc)相似文献   

Energy absorption in time-dependent unitary random matrix ensembles: Dynamic versus anderson localization

JETP Letters - We consider energy absorption in an externally driven complex system of noninteracting fermions with the chaotic underlying dynamics described by the unitary random matrices. In the...     

Complexes of marked graphs in gauge theory

Letters in Mathematical Physics - We review the gauge and ghost cyle graph complexes as defined by Kreimer, Sars and van Suijlekom in “Quantization of gauge fields, graph polynomials and...     

Anderson localization for radial tree-like random quantum graphs

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables (iid). For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.     

Susceptibility and specific heat of intermediate valence compounds studied in mean-field theory of a periodic anderson model

The periodic Anderson model for a lattice of magnetic ions is investigated in Hartree-Fock approximation. Attention is paid to different solutions of the self-consistency equations corresponding to ferromagnetic or antiferromagnetic ordering of the local magnetic moments. The effect of hybridization leading to reduced magnetic moments strongly depends on the position of the localizedf levels relative to the conduction band. For paramagnetic solutions with a non-integer value for thef level occupation number comparison is made with properties of intermediate valence rare earth compounds. The mean-field results for the susceptibility and specific heat agree with essential features found for these substances.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Circuit based graphs for renormalized perturbation theory

A generalization of graph theory is introduced and used to obtain Feynman parametric formulas relevant to renormalized amplitudes. The generalization of graph theory is based upon circuit coefficients instead of the usual incidence matrix. The parametric formulas presented are valid for amplitudes which have been renormalized, as in the Zimmermann formulation, by subtracting Taylor terms in momentum space.The research reported in this paper was supported in part by the Max-Planck-Institut für Physik, München, by the German and American Fulbright Commission in Bonn, and by the Department of Mathematics of the University of Virginia, Charlottesville.     

Aging effects in an anderson insulator

Aging, commonly observed in glasses, is a manifestation of breakdown of time-translational invariance. Here we demonstrate experimentally aging effects in the electronic system of an Anderson insulator. The aging phenomenon in the electron glass appears to be much less sensitive to temperature than in other systems. The differences in the behavior of the electron glass and a spin glass system are discussed in terms of some microscopic differences between the two systems.     

Equity trees and graphs via information theory

We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the “genus 0” condition recently introduced in order to study the networks of equities.