Spectral behavior of quasi periodic potentials
Abstract
Spectral properties of Schrödinger operators of the typeHɛ=-Δ+ɛV, where Δ is the Laplacian,V a quasiperiodic potential and ɛ a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small ɛ a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as ɛ is increased.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- September 1982
- DOI:
- Bibcode:
- 1982CMaPh..84..377S
- Keywords:
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- Neural Network;
- Statistical Physic;
- Complex System;
- Nonlinear Dynamics;
- Spectral Property