Acoustic characterization of the Hofstadter butterfly with resonant scatterers
Laboratoire d'Acoustique de l'Université du Maine UMR CNRS 6613
Avenue O. Messiaen, 72085 Le Mans Cedex 9, France
Accepted: 3 April 2002
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 distributed 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.
PACS: 43.20.Fn – Scattering of acoustic waves / 43.20.Mv – Waveguides, wave propagation in tubes and duct / 43.58.Gn – Acoustic impulse analyzers and measurements
© EDP Sciences, 2002