Erratum: Photonic heterostructures with Lévy-type disorder: Statistics of coherent transmission [Phys. Rev. A<b>85</b>, 035803 (2012)]

Fernández-Marín, A. A.; Méndez-Bermúdez, J. A.; Gopar, Víctor A.

doi:10.1103/physreva.87.039908

Cited by 10 publications

(15 citation statements)

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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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Section: Introductionmentioning

confidence: 99%

Localization in one-dimensional chains with Lévy-type disorder

2015

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“…( 9). Similarly, a power-law is found for the average transmission [17] T ∝ L −α in contrast to the exponentially decay for standard disordered systems in Eq. ( 8).…”

Section: Statistics Of the Intensity Inside 1d Media With L éVy Disordermentioning

confidence: 60%

“…The numerical simulations performed in this work are based on the transfer matrix approach [17,34]. The numerical model consists of layers of thickness 2.5 mm with refraction index n 2 = 1.1, and reflection coefficient 0.007, randomly placed in a background of index of refraction n 1 = 1 with separations following a Gaussian distribution for standard disorder and a Lévy α-stable distribution for Lévy disorder.…”

Section: B Statistics Of the Transmission In Standard Disordered 1d M...mentioning

confidence: 99%

“…In Lévy-type disorder, waves can travel long distances without being scattered and thus have a profound impact on the transport properties. Measurements and analytic calculations of wave transmission in Lévy α-stable media give different scaling than in standard 1D random media [8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Statistics of coherent waves inside media with Lévy disorder

Razo-López,

Genack,

Gopar

2021

Preprint

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Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the study of wave propagation or lasing in such systems requires the consideration of coherent scattering. We consider the distribution of wave energy inside 1D random media in which the spacing between scatterers follow a Lévy α-stable distribution characterized by a power-law decay with exponent α. We show that the averages of the intensity and logarithmic intensity are given in terms of the average of the logarithm of transmission and the depth into the sample raised to the power α. Mapping the depth into the sample to the number of scattering elements yields intensity statistics that are identical to those found for Anderson localization in standard random media. This allows for the separation for the impacts of disorder distribution and wave coherence in random media.

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“…Motivated by the realization of experimentally controlled Lévy processes in the so-called Lévy glasses, 32 in Ref. [27] a model was developed to describe the statistical properties of the conductance through a 1D quantum wire where electrons suffer multiple scattering due to scatterers placed along the wire in a random way accordingly to a Lévy-type distribution (see [33][34][35][36][37] for other examples where Lévy processes have been studied in connection to transport problems). It was found in [27] that the full statistics of the conductance is determined by the average ln g and the exponent α of power-law tail in the macroscopic limit (L ≫ c 1/α ).…”

Section: Theoretical Modelmentioning

confidence: 99%

Conductance of one-dimensional quantum wires with anomalous electron wave-function localization

et al. 2012

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We study the statistics of the conductance g through one-dimensional disordered systems where electron wavefunctions decay spatially as |ψ| ∼ exp(−λr α ) for 0 < α < 1 , being a constant. In contrast to the conventional Anderson localization where |ψ| ∼ exp(−λr) and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized (α < 1) the full statistics of the conductance is determined by the average ln g and the power α. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value α = 1/2. To test our theory for other values of α, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.

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Erratum: Photonic heterostructures with Lévy-type disorder: Statistics of coherent transmission [Phys. Rev. A85, 035803 (2012)]

Cited by 10 publications

References 0 publications

Localization in one-dimensional chains with Lévy-type disorder

Localization in one-dimensional chains with Lévy-type disorder

Statistics of coherent waves inside media with Lévy disorder

Conductance of one-dimensional quantum wires with anomalous electron wave-function localization

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