Anderson transition and minimum metallic conductivity in disordered two-dimensional systems

Scher, G.

doi:10.1016/0022-3093(83)90518-5

Cited by 20 publications

(3 citation statements)

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“…It will not be out of place to state here that the approximations involved in the scaling theory [l] have recently been questioned [13,14]. Also, there are some other independent arguments [15, 161 that deny the validity of the result [l].…”

Section: Discussionmentioning

confidence: 99%

The case of disordered two‐dimensional electron systems

Srivastava

1986

Int J of Quantum Chemistry

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We investigate the question of the existence or nonexistence of mobility edges that separate the localized and extended states in two-dimensional disordered electron systems treated within the Anderson model. Evidence is produced to show that the mobility edges exist if the amount of disorder is less than a critical value. The following three different agruments are presented: (1) exact enumeration of self-avoiding walks that contribute to the renormalized perturbation series of self-energy whose convergence (divergence) indicates localization (delocalization); (2) "quantum percolation" in a strongly disordered binary alloy; and (3) influence of magnetic field on localized and extended states (the quantum Hall Effect problem).

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Section: Discussionmentioning

confidence: 99%

The case of disordered two‐dimensional electron systems

Srivastava

1986

Int J of Quantum Chemistry

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“…dimensions greater than one is confined to the work by Weaver [12], and, inasmuch as measurements of frequency-frequency intensity correlation functions imply measurements of time domain behavior, that of Genack and Garcia[10,11]. Numerical work in the time domain is reported by Prelovsek [20], Scher [21 ), Shore and Halley [22], Weaver and Loewenherz [23], Weaver [16], and Vanneste et a/. [24].…”

Section: Experimental Work In the Time Domain On Anderson Localization And Anomalous Diffusion Inmentioning

confidence: 99%

“…where the bold index n runs over the sites of a large square lattice. The sum is over the four nearest neighbor sites m of site n, and kn is five plus a random number taken from the uniform distribution The evolution of systems like that of equation(S} from specified narrow-band initial conditions has been studied previously [20,21 ]. In this work we numerically study the evolution dictated by equation (1} rather than, like Prelovsek [20] and Scher [21 ], equation (5).…”

Section: Numerical Modelmentioning

confidence: 99%

Anderson localization in the time domain: Numerical studies of waves in two-dimensional disordered media

Weaver

1993

The Journal of the Acoustical Society of America

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A numerical model for the dynamics of a classical wave equation in a two dimensional Anderson disordered medium is integrated over times of the order of 27000 inverse band widths.Excitations by narrow band sources lead to wave energy densities whose ensemble averages behave diffusively at early times. The behavior at more general times and distances is, however, not diffusive. The observed transport profiles are shown to be inconsistent with predictions from the hydrodynamical continuum model of Anderson localization, and to the hypothesis of exponentially slow diffusion. The evolution of the energy density distribution in systems with varying disorders and microstructures, and over a range of length scales, is found to collapse to a single function of rescaled space and time well approximated by e(x,t) = exp{-x/1; -(x2+n/4 p i;n t)P } with n= 0.46, p= .76, where x is the distance from the source, I; is the localization length and the p is a "residual diffusivity" not equal to the bare diffusivity. Dissipation is shown to have no de-localizing effect.

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Quantum Percolation: Meaning and Results

Srivastava

1987

Time-Dependent Effects in Disordered Materials

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Anderson transition and minimum metallic conductivity in disordered two-dimensional systems

Cited by 20 publications

References 4 publications

The case of disordered two‐dimensional electron systems

The case of disordered two‐dimensional electron systems

Anderson localization in the time domain: Numerical studies of waves in two-dimensional disordered media

Quantum Percolation: Meaning and Results

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