Scientific Results

Localization in one-dimensional chains with Lévy-type disorder

Year: 2015

Authors: Zakeri S.S., Lepri S., Wiersma D.

Autors Affiliation: European Laboratory for Non-linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, Sesto Fiorentino, I-50019, Italy; Consiglio Nazionale Delle Ricerche, Istituto Dei Sistemi Complessi, via Madonna del Piano 10, Sesto Fiorentino, I-50019, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via Giovanni Sansone 1, Sesto Fiorentino, I-50019, Italy; Consiglio Nazionale Delle Ricerche, Istituto Nazionale di Ottica, Largo Fermi 6, Firenze, I-50125, Italy; Universit√° di Firenze, Dipartimento di Fisica e Astronomia, via Giovanni Sansone 1, Sesto Fiorentino, I-50019, Italy

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+alpha)) with s as the distance between two successive impurities and alpha > 0. This model of disorder is long-range correlated and is inspired by the peculiar structure of the complex optical systems known as Levy 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 xi(alpha)(omega) similar to omega(-alpha). 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 alpha-dependent exponent which can be estimated analytically.

Journal/Review: PHYSICAL REVIEW E

Volume: 91 (3)      Pages from: 032112-1  to: 032112-9

More Information: Authors wish to thank Mario Mulansky for assistance with the manuscript and are grateful for the financial support from the European Research Council (FP7/2007-2013), ERC Grant No. 291349.
KeyWords: Condensed matter physics, Anderson localization; Complex optical systems; Frequency behavior; Localization length; Localized wave packets; One-dimensional chains; Physical interpretation; Theoretical arguments, Chains
DOI: 10.1103/PhysRevE.91.032112

Citations: 12
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