Acoustic characterization of Hofstadter butterfly with resonant scatterers

TL;DR

This paper experimentally investigates the Hofstadter butterfly phenomenon using acoustic waves and resonant scatterers, demonstrating how resonances influence the transmission spectrum's complex band structure.

Contribution

It introduces an experimental setup for acoustic realization of the Hofstadter butterfly with variable resonant scatterers and compares experimental results with analytical and computational models.

Findings

Forbidden band structures reproduce the Hofstadter butterfly pattern.

Resonances of scatterers significantly affect the butterfly's structure.

Experimental results align with theoretical and computational predictions.

Abstract

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly.