Absence of localisation in the almost Mathieu equation
- 1 January 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (1) , L21-L23
- https://doi.org/10.1088/0305-4470/20/1/005
Abstract
The author considers the discrete Schrodinger operator on Z with the potential lambda cos 2 pi ( alpha n+ theta ). This one-dimensional model occurs in the study of an electron in a two-dimensional periodic potential with a uniform magnetic field. First it is proved that for every alpha and for lambda 2(Z) but are not summable.Keywords
This publication has 9 references indexed in Scilit:
- Absence of localization in a class of Schrödinger operators with quasiperiodic potentialCommunications in Mathematical Physics, 1986
- Franco-American meeting on the mathematics of random and almost periodic potentialsJournal of Statistical Physics, 1984
- Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d’un théorème d’Arnold et de Moser sur le tore de dimension 2Commentarii Mathematici Helvetici, 1983
- A metal-insulator transition for the almost Mathieu modelCommunications in Mathematical Physics, 1983
- Almost periodic Schrödinger operators II. The integrated density of statesDuke Mathematical Journal, 1983
- Almost periodic Schrödinger operators: A ReviewAdvances in Applied Mathematics, 1982
- Singular continuous spectrum for a class of almost periodic Jacobi matricesBulletin of the American Mathematical Society, 1982
- Spectral properties of disordered systems in the one-body approximationCommunications in Mathematical Physics, 1980
- Topological transitivity of one class of dynamic systems and flows of frames on manifolds of negative curvatureFunctional Analysis and Its Applications, 1975