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In addition to the basic crystalline and amorphous structures for solids, it is possible that solids may also form with a quasiperiodic, or Penrose tile, structure. A current problem in condensed-matter physics is to determine how this structure affects the various physical properties of a material. A fundamental question involves the consequences of quasiperiodic symmetry in the eigenvalue spectrum and eigenfunctions of a wave equation. While rigorous theorems have been derived for one-dimensional systems, there is currently no known “quasi-Bloch theorem” for two and three dimensions. To gain insight into this problem, an acoustic experiment has been used to study a two-dimensional wave system with a Penrose tile symmetry. The results show an eigenvalue spectrum containing bands and gaps with widths which are in the ratio of the Golden Mean, (√5 + 1)/2.
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