Eigenvalue spectrum, density of states, and eigenfunctions in a two-dimensional quasicrystal
- 17 April 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 62 (16) , 1888-1891
- https://doi.org/10.1103/physrevlett.62.1888
Abstract
In this Letter we report the experimental determination of the eigenvalue spectrum, density of states, and individual eigenfunctions in an acoustic system analogous to a two-dimensional Schrödinger equation with a quasiperiodic (Penrose tile) potential. The results show features unique to the quasiperiodic symmetry, such as the appearance of gaps and bands with widths which are in the ratio of the golden mean (√5 +1)/2.Keywords
This publication has 27 references indexed in Scilit:
- Growing Perfect QuasicrystalsPhysical Review Letters, 1988
- Scale equivalence of quasicrystallographic space groupsPhysical Review B, 1988
- Quasicrystals. I. Definition and structurePhysical Review B, 1986
- Quasicrystals. II. Unit-cell configurationsPhysical Review B, 1986
- Phonon spectra in one-dimensional quasicrystalsJournal of Statistical Physics, 1986
- Metallic Phase with Long-Range Orientational Order and No Translational SymmetryPhysical Review Letters, 1984
- Renormalization-group analysis of the discrete quasiperiodic Schrödinger equationPhysical Review B, 1984
- One-Dimensional Schrödinger Equation with an Almost Periodic PotentialPhysical Review Letters, 1983
- Localization Problem in One Dimension: Mapping and EscapePhysical Review Letters, 1983
- Almost periodic Schrödinger operators: A ReviewAdvances in Applied Mathematics, 1982