Localization and resonant transmission of third-sound waves on a random substrate

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Abstract
The analysis of a recently proposed experiment, designed to study the one-dimensional localization of third-sound excitations, is extended to higher frequencies. Transmission resonances are predicted for a discrete set of frequencies. The disorder is introduced by randomly distributing identical parallel strips of a modified substrate. These strips can be produced in such a way that they either modify the thickness of the part of the superfluid film located on the strips or change the effective third-sound speed in these regions. The main features of the localization and the transmission resonances are studied in detail. The system described here is shown to be conceptually far simpler than its electronic analogs. Experimentally, the analogs of inelastic scattering and interaction effects in the electron problem can be easily controlled.