Multifractal spectral and wave-function properties of the quasiperiodic modulated-spring model
- 15 September 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 38 (9) , 5811-5820
- https://doi.org/10.1103/physrevb.38.5811
Abstract
A method is discussed to analyze multifractal properties of spectra and wave functions by means of an entropy function. The method is exemplified on a model for lattice vibrations in an incommensurate crystal phase. It is shown that the model has a spectrum with scaling properties. Moreover, it is probably singular continuous, which is a rather exceptional case. This is even true when the spectrum becomes a fat fractal. The scaling properties of the mode wave functions are discussed.Keywords
This publication has 20 references indexed in Scilit:
- Modulated Kronig-Penney model in superspacePhysica A: Statistical Mechanics and its Applications, 1984
- Renormalization-group analysis of the discrete quasiperiodic Schrödinger equationPhysical Review B, 1984
- Localization inv-dimensional incommensurate structuresCommunications in Mathematical Physics, 1983
- Metal-Insulator Transition and Scaling for Incommensurate SystemsPhysical Review Letters, 1983
- Electrons in incommensurate crystals: Spectrum and localizationPhysical Review B, 1983
- One-Dimensional Schrödinger Equation with an Almost Periodic PotentialPhysical Review Letters, 1983
- Localization Problem in One Dimension: Mapping and EscapePhysical Review Letters, 1983
- Quasiperiodic interaction with a metal-insulator transitionPhysical Review B, 1982
- Singular continuous spectrum for a class of almost periodic Jacobi matricesBulletin of the American Mathematical Society, 1982
- Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fieldsPhysical Review B, 1976