On the statistics of superlocalized states in self-affine disordered potentials
| dc.creator | Luck, J. M. | |
| dc.date | 2004-09-06 | |
| dc.date.accessioned | 2026-07-07T03:00:19Z | |
| dc.date.available | 2026-07-07T03:00:19Z | |
| dc.description | We investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples much larger than a well-defined crossover length, which diverges in the weak-disorder regime. We present a parallel analytical investigation of the statistics of these superlocalized states in the discrete and the continuum formalisms. For the discrete tight-binding model, the effective localization length decays logarithmically with the sample size, and the logarithm of the transmission is marginally self-averaging. For the continuum Schrödinger equation, the superlocalization phenomenon has more drastic effects. The effective localization length decays as a power of the sample length, and the logarithm of the transmission is fully non-self-averaging. | |
| dc.description | 21 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0409117 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0409117 | |
| dc.identifier | J. Phys. A 38 (2005) 987-1003 | |
| dc.identifier | doi:10.1088/0305-4470/38/5/002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/24791 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | On the statistics of superlocalized states in self-affine disordered potentials | |
| dc.type | text |