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Extended states for the Schrödinger operator with quasi-periodic potential in dimension two /
The authors consider a Schrödinger operator H=-\Delta +V(\vec x) in dimension two with a quasi-periodic potential V(\vec x). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the follo...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1239. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | The authors consider a Schrödinger operator H=-\Delta +V(\vec x) in dimension two with a quasi-periodic potential V(\vec x). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves e^i\langle \vec \varkappa, \vec x\rangle in the high energy region. Second, the isoenergetic curves in the space of momenta \vec \varkappa corresponding to these eigenfunctions have the form of slightly distorted circles with holes. |
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| Descripción Física: | 1 online resource (v, 139 pages) |
| Bibliografía: | Includes bibliographical references. |
| ISBN: | 9781470450694 1470450690 |
| ISSN: | 0065-9266 ; |