Anomalous localization in low-dimensional systems with correlated disorder

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig–Penney models with different types of perturbations. Main attention is paid to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides.     

Anderson localization in 1D systems with correlated disorder

Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the localization length and the density of states and compare our numerical results with analytical predictions. Specifically, we find two distinct characteristic behaviors in the vicinity of the band center and at the unperturbed band edge, respectively. Furthermore we address the effect of the intrinsic short-range correlations.     

Periodic-orbit theory of anderson localization on graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.     

Mass of a short-range correlated nucleon

Nucleon properties and structure should be modified by short-range correlations(SRC) among nucleons.By analyzing SRC ratio data, we extract the mass of a nucleon in an SRC pair and the expected number of pn-SRC pairs in deuterium, under the assumption that the SRC nucleon mass is universal for different nuclei. The nucleon mass of a two-nucleon SRC pair is m_(SRC)= 852 ± 18 MeV, and the number of pn-SRC pairs in deuterium is ~(n~d)SRC=0.021 ± 0.005. The mass deficit of the strongly overlapping nucleon can be explained by the trace anomaly contribution to the mass in QCD or alternatively by the vacuum energy in the MIT bag model.     

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.     

Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.     

Superconducting properties of the anderson model with correlated electron off-site attraction

Summary Using the Green's function method, the superconducting gap equation in the Anderson model with nearest-enighbour attraction between correlated electrons is obtained. Thes- andp-wave solutions of this equation have been analysed for different choices of the parameters of the model. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

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   

Absence of localization on the 2d model with long-range correlated off-diagonal disorder

We study the one-electron eigenstates in atwo-dimensional (2d) Anderson model with long-range correlated off-diagonaldisorder, generated by a 2ddiscrete Fourier method. The dynamics of an initiallylocalized wave packet is investigated by numerically solving the2d time-dependent Schrödinger equation. In additional the participation number and itsscaling behavior was obtained through direct diagonalization. Our numerical data suggest that the systemexhibits a ballistic dynamics in the stronglycorrelated disorder regime. Moreover, the scaling analysis of mean participation number around the band centeralso indicates the presence of extended states for high degree of correlations.     

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.     

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...