Multi-fractal spectra and wavefunctions of one-dimensional quasi-crystals
- 30 May 1987
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 20 (15) , L295-L302
- https://doi.org/10.1088/0022-3719/20/15/002
Abstract
The electronic structure of a quasi-crystalline lattice generated by almost-periodic tilings of the line is examined. The author finds that the wavefunctions and the spectra are characterised by a continuous set of scaling indices and calculates their alpha -f( alpha ) spectrum. Eigenfunctions at special energies are considered in detail. The spectral scaling properties are compared with previous results for spectral dimensions valid near the band centre and the band edges.Keywords
This publication has 19 references indexed in Scilit:
- Global scaling properties of the spectrum for a quasiperiodic schrödinger equationPhysical Review B, 1986
- Quasiperiodic lattice: Electronic properties, phonon properties, and diffusionPhysical Review B, 1986
- Electronic and vibrational spectra of two-dimensional quasicrystalsPhysical Review B, 1986
- Fractal measures and their singularities: The characterization of strange setsPhysical Review A, 1986
- Phonon spectra in one-dimensional quasicrystalsJournal of Statistical Physics, 1986
- Quasicrystals: A New Class of Ordered StructuresPhysical Review Letters, 1984
- 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