Lifshitz tails in the 3D Anderson model
| dc.creator | Elgart, Alexander | |
| dc.date | 2008-04-21 | |
| dc.date.accessioned | 2026-07-07T09:33:47Z | |
| dc.date.available | 2026-07-07T09:33:47Z | |
| dc.description | Consider the 3D Anderson model with a zero mean and bounded i.i.d. random potential. Let $λ$ be the coupling constant measuring the strength of the disorder, and $σ(E)$ the self energy of the model at energy $E$. For any $ε>0$ and sufficiently small $λ$, we derive almost sure localization in the band $E \le -σ(0)-λ^{4-ε}$. In this energy region, we show that the typical correlation length $ξ_E$ behaves roughly as $O((|E|-σ(E))^{-1/2})$, completing the argument outlined in the unpublished work of T. Spencer. | |
| dc.description | 24 pages, 3 figures, to appear in DMJ | |
| dc.identifier | https://arxiv.org/abs/0804.3347 | |
| dc.identifier | http://arxiv.org/abs/0804.3347 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159256 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B44,47B80,81Q10,81T18,81T15 | |
| dc.title | Lifshitz tails in the 3D Anderson model | |
| dc.type | text |