Anderson localization in finite 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, measured using these wave amplitudes, decreases as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. From the spectrum, the nearest-neighbor spacing distribution can be obtained. This distribution can be described by a phenomenological expression that depends on a parameter α, related to the level repulsion, which is also a function of the frequency. Therefore, the localization length can be expressed in terms of the parameter α. There exists a range in which the localization length grows linearly with α. However, at low values of this parameter the linear dependence does not hold.