On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators
We study spectral properties of a family of quasiperiodic Schrödinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curve has a real branch that is extended along the momentum direction. In the energy intervals where this happens, we obtain an asymptot...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/145436 |
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| Summary: | We study spectral properties of a family of quasiperiodic Schrödinger
operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic
curve has a real branch that is extended along the momentum direction. In the energy intervals
where this happens, we obtain an asymptotic formula for the Lyapunov exponent and show
that the spectrum is purely singular. This result was conjectured and proved in a particular
case by Fedotov and Klopp (2005). |
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| ISSN: | 1687-9120 1687-9139 |