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

Abstract

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.

arXiv comment7 pages,7 figures

References in corpus (10)

• Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Mobility Edge in Aperiodic Kronig-Penney Potentials with Correlated Disorder: Perturbative Approach
• Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides
• Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport
• Localization in one-dimensional chains with Lévy-type disorder
• Lyapunov exponents in 1d disordered system with long-range memory
• Irrational anomalies in one-dimensional Anderson localization
• Quantum Diffusion and Localization in Disordered Electronic Systems
• Localization and delocalization in one-dimensional systems with translation-invariant hopping