Third-Sound Propagation in a Thue-Morse Lattice

Resonant transmission and velocity renormalization of third sound in one-dimensional random lattices

“…The wave propagation in ID quasiperiodic systems (Fibonacci lattice) [6][7][8][9] has also been studied, having in mind the close relation to the properties of real quasicrystals [10]. The Thue-Morse lattice is another nonperiodic system studied, an arrangement that is neither periodic, quasiperiodic, nor random [11,12]. These phenomena have the same origin as the Bragg scattering in a periodic system, namely, multiple scattering and interference.…”

“…The experimental method for the study of the third-sound propagation in modulated 1D media has been developed by Smith et al [5,17,18]. We have developed a similar technique independently [9, 12,19]. The original ideas of our method are to be credited to Condat and Kirkpatrick (CK) [1,20].…”

“…In addition, the measurement was done at 0.8 K to reduce the attenuation effect. The experimental details are described elsewhere [12].…”

“…In this sense, the Thue-Morse lattice is closer to the homogeneous medium than the periodic or the Fibonacci lattice. A simple relation holds between the positions of these dips [12]. The detailed properties of these spectra are discussed elsewhere [9, 12,19].…”