Localization of acoustic waves

Abstract

The localization of sound waves moving in a random array of hard scatterers is studied for both two- and three-dimensional systems using a diagrammatic technique. For d=2 acoustic waves are found to be localized for all frequencies with the localization length growing exponentially for both high and low frequencies. For d=3 there are mobility edges at an intermediate frequency and at a high frequency. Between these mobility edges the sound waves are localized. The connection between this problem and quantum-mechanical electron localization is discussed.