Localization lengths for Schroedinger operators on Z^2 with decaying random potentials
| dc.creator | Chen, Thomas | |
| dc.date | 2005-03-28 | |
| dc.date | 2005-10-26 | |
| dc.date.accessioned | 2026-07-07T07:49:20Z | |
| dc.date.available | 2026-07-07T07:49:20Z | |
| dc.description | We study a class of Schrödinger operators on $\Z^2$ with a random potential decaying as $|x|^{-\dex}$, $0<\dex\leq\frac12$, in the limit of small disorder strength $λ$. For the critical exponent $\dex=\frac12$, we prove that the localization length of eigenfunctions is bounded below by $2^{λ^{-\frac14+η}}$, while for $0<\dex<\frac12$, the lower bound is $λ^{-\frac{2-η}{1-2\dex}}$, for any $η>0$. These estimates "interpolate" between the lower bound $λ^{-2+η}$ due to recent work of Schlag-Shubin-Wolff for $\dex=0$, and pure a.c. spectrum for $\dex>\frac12$ demonstrated in recent work of Bourgain. | |
| dc.description | AMS Latex, 26 pages, 1 Figure. Final version. To appear in Int. Math. Res. Notices | |
| dc.identifier | https://arxiv.org/abs/math-ph/0503064 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0503064 | |
| dc.identifier | Int. Math. Res. Notices, 2005:54, 3341-3373 (2005). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124806 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81Q10 | |
| dc.title | Localization lengths for Schroedinger operators on Z^2 with decaying random potentials | |
| dc.type | text |