Internal Lifshitz tails for discrete Schrödinger operators
We consider random Schrödinger operators Hω acting on l2(ℤd). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states of Hω has a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated d...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/91865 |
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| _version_ | 1832566748566519808 |
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| author | Hatem Najar |
| author_facet | Hatem Najar |
| author_sort | Hatem Najar |
| collection | DOAJ |
| description | We consider random Schrödinger operators Hω acting on l2(ℤd). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states of Hω has a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated density of states of a well-chosen periodic operator is nondegenerate at the same edges. A possible application of the result to get Anderson localization is given. |
| format | Article |
| id | doaj-art-3a94a0ce190f44eca5e1cb2cecf396a5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3a94a0ce190f44eca5e1cb2cecf396a52025-02-03T01:03:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/9186591865Internal Lifshitz tails for discrete Schrödinger operatorsHatem Najar0Département de Mathématiques Physiques, I.P.E.I. Monastir, Monastir 5000, TunisiaWe consider random Schrödinger operators Hω acting on l2(ℤd). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states of Hω has a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated density of states of a well-chosen periodic operator is nondegenerate at the same edges. A possible application of the result to get Anderson localization is given.http://dx.doi.org/10.1155/IJMMS/2006/91865 |
| spellingShingle | Hatem Najar Internal Lifshitz tails for discrete Schrödinger operators International Journal of Mathematics and Mathematical Sciences |
| title | Internal Lifshitz tails for discrete Schrödinger operators |
| title_full | Internal Lifshitz tails for discrete Schrödinger operators |
| title_fullStr | Internal Lifshitz tails for discrete Schrödinger operators |
| title_full_unstemmed | Internal Lifshitz tails for discrete Schrödinger operators |
| title_short | Internal Lifshitz tails for discrete Schrödinger operators |
| title_sort | internal lifshitz tails for discrete schrodinger operators |
| url | http://dx.doi.org/10.1155/IJMMS/2006/91865 |
| work_keys_str_mv | AT hatemnajar internallifshitztailsfordiscreteschrodingeroperators |