title: Localization in one-dimensional chains with Lévy-type disorder.
abstract: 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.
authors: European Laboratory for Non-linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.
authors: Sepideh S
authors: SS
authors: Zakeri
authors: Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.|Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy.
authors: Stefano
authors: S
authors: Lepri
authors: European Laboratory for Non-linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.|Consiglio Nazionale delle Ricerche, Istituto Nazionale di Ottica, Largo Fermi 6, I-50125 Firenze, Italy.|Universitá di Firenze, Dipartimento di Fisica e Astronomia, via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy.
authors: Diederik S
authors: DS
authors: Wiersma