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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832556017737531392 |
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| author | Magali Marx Hatem Najar |
| author_facet | Magali Marx Hatem Najar |
| author_sort | Magali Marx |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-c54bb5915b3a4ea3bfe0c70de3530fc5 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-c54bb5915b3a4ea3bfe0c70de3530fc52025-02-03T05:46:37ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/145436145436On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger OperatorsMagali Marx0Hatem Najar1LAGA, U.M.R. 7539 C.N.R.S, Institut Galilée, Université de Paris-Nord, 99 Avenue J.-B. Clément, 93430 Villetaneuse, FranceDépartement de Mathématiques, I.S.M.A.I. Kairouan, Abd Assed Ibn Elfourat, 3100 Kairouan, TunisiaWe 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).http://dx.doi.org/10.1155/2010/145436 |
| spellingShingle | Magali Marx Hatem Najar On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators Advances in Mathematical Physics |
| title | On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators |
| title_full | On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators |
| title_fullStr | On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators |
| title_full_unstemmed | On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators |
| title_short | On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators |
| title_sort | on the singular spectrum for adiabatic quasiperiodic schrodinger operators |
| url | http://dx.doi.org/10.1155/2010/145436 |
| work_keys_str_mv | AT magalimarx onthesingularspectrumforadiabaticquasiperiodicschrodingeroperators AT hatemnajar onthesingularspectrumforadiabaticquasiperiodicschrodingeroperators |