Quantum diffusion and localization in disordered electronic systems

Wells, P. R.; Castro, J. d'Albuquerque e; Queiroz, S. L. A. de

doi:10.1103/physrevb.78.035102

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…The effects of Cauchy distribution on Anderson localization were studied in [26,27], while the conductance properties through quantum wires were considered in [28,29]. The effects of the long-range correlated potential on Anderson localization were considered in [30][31][32][33][34], while the effects of the Brewster anomaly were investigated numerically in [35].…”

Section: Introductionmentioning

confidence: 99%

Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices

Asatryan

Novikov

2018

Phys. Rev. B

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Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices is studied analytically and numerically. The disordered medium is composed of layers with alternating refractive indices and with thickness disorder distributed according to the Pareto distribution ∼1/x (α+1) . In Levy lattices the variance (or both variance and mean) of a random parameter does not exist, which leads to a different functional form for the localization length. In this study an equation for the localization length is obtained, and it is found to be in excellent agreement with the numerical calculations throughout the spectrum. The explicit asymptotic equations for the localization lengths for both short and long wavelengths have been deduced. It is shown that the localization length tends to a constant at short wavelengths and it is determined by the layer interface Fresnel coefficient. At the long wavelengths the localization length is proportional to the power of the wavelength ∼ λ α for 1 < α < 2, and it has a transcendental behavior ∼ λ 2 / ln λ for α = 2. For α > 2, where the variance of the random distribution exists, the localization length attains its classical long-wavelength asymptotic form ∼ λ 2 .

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Section: Introductionmentioning

confidence: 99%

Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices

Asatryan

Novikov

2018

Phys. Rev. B

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“…Although our main motivation stems from the above described setup, it is worth mentioning some related studies of systems with Lévy-type disorder that include transport in quantum wires [5], photonic heterostructures [6], and disordered electronic systems [7,8]. The purpose of this work is to provide a framework to investigate localization in power-law correlated disordered systems and to illustrate how the localization length is affected by different characteristic features of the system such as frequency, degree of heterogeneity, disorder strength, etc.…”

Section: Introductionmentioning

confidence: 99%

Localization in one-dimensional chains with Lévy-type disorder

2015

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We study Anderson localization of the classical lattice waves in a chain with mass impurities distributed randomly through a power-law relation s-(1+α) with s as the distance between two successive impurities and α>0. This model of disorder is long-range correlated and is inspired by the peculiar structure of the complex optical systems known as Lévy glasses. Using theoretical arguments and numerics, we show that in the regime in which the average distance between impurities is finite with infinite variance, the small-frequency behavior of the localization length is ξ{ω)∼ω-α. The physical interpretation of this result is that, for small frequencies and long wavelengths, the waves feel an effective disorder whose fluctuations are scale dependent. Numerical simulations show that an initially localized wave-packet attains, at large times, a characteristic inverse power-law front with an α-dependent exponent which can be estimated analytically.

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“…Our approach provides a systematic way of calculating the higher orders of perturbation expansion with any given distribution of spacing between impurities. In this paper, we study the problem of electron localization [10][11][12] although mathematically it is equivalent to the problem of mechanical vibrations.…”

Section: Introductionmentioning

confidence: 99%

Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass

Sepehrinia

2022

Preprint

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We have studied the localization of waves in a one-dimensional lattice consisting of impurities where the spacing between consecutive impurities can take certain values with given probabilities. In general, such a distribution of impurities induces correlations in the disorder. In particular with a power-law distribution of spacing, this system is used as a model for light propagation in Lévy glasses. We introduce a method of calculating the Lyapunov exponent which overcomes limitations in the previous studies and can be easily extended to higher orders of perturbation theory. We obtain the Lyapunov exponent up to fourth order of perturbation and discuss the range of validity of perturbation theory, transparent states, and anomalous energies which are characterized by divergences in different orders of the expansion. We also carry out numerical simulations which are in agreement with our analytical results.

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Quantum diffusion and localization in disordered electronic systems

Cited by 6 publications

References 25 publications

Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices

Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices

Localization in one-dimensional chains with Lévy-type disorder

Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass

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