Anderson Localization in Disordered Vibrating Rods
Abstract
We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.
Cite
@article{arxiv.1203.4241,
title = {Anderson Localization in Disordered Vibrating Rods},
author = {J. Flores and L. Gutiérrez and R. A. Méndez-Sánchez and G. Monsivais and P. Mora and A. Morales},
journal= {arXiv preprint arXiv:1203.4241},
year = {2015}
}
Comments
10 pages, 6 figures