Exact analytic solution of the multi-dimensional Anderson localization
| dc.creator | Kuzovkov, V. N. | |
| dc.creator | von Niessen, W. | |
| dc.date | 2004-02-18 | |
| dc.date.accessioned | 2026-07-07T02:56:32Z | |
| dc.date.available | 2026-07-07T02:56:32Z | |
| dc.description | The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $<ψ^2_{n,\mathbf{m}}>$, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes: low-dimensional systems ($2\leq D \leq 3$), where localized states are always exponentially localized and high-dimensional systems ($D\geq D_c=4$), where states with non-exponential localization are also formed. The value of the upper critical dimension is found to be $D_0=6$ for the Anderson localization problem; this value is also characteristic of a related problem - percolation. Consequences for numerical scaling and other approaches are discussed in detail. | |
| dc.description | 25 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0402463 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0402463 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/23361 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Exact analytic solution of the multi-dimensional Anderson localization | |
| dc.type | text |