Resonant enhancement of Anderson localization: Analytical approach

Abstract

We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization, is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between wells/barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. We also discuss whether the single parameter scaling is valid in view of the suggested modification of the theory. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.

11 pages, 10 figures

References in corpus (15)

• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Band-center anomaly of the conductance distribution in one-dimensional Anderson localization
• Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder
• Anderson localization in metamaterials and other complex media
• Matter Wave Transport and Anderson Localization in Anisotropic 3D Disorder
• From closed to open 1D Anderson model: Transport versus spectral statistics
• Anderson localization of matter waves in tailored disordered potentials
• Anomalous properties of the Kronig-Penney model with compositional and structural disorder
• Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach
• Non-Conventional Anderson Localization in Bilayered Structures with Metamaterials
• Localization length of nearly periodic layered metamaterials
• Short-distance wavefunction statistics in one-dimensional Anderson localization
• Anderson Localization in Metamaterials with Compositional Disorder
• Wave transport in one-dimensional disordered systems with finite-width potential steps
• Non-conventional Anderson localization in a matched quarter stack with metamaterials

Cited by in corpus (5)

• Anomalous mobility edges in one-dimensional quasiperiodic models
• Transport through quasi-one-dimensional wires with correlated disorder
• Wave Transport in One-Dimensional Disordered Systems with Finite-Size Scatterers
• Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach
• Resonant Anderson localization in segmented wires