Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime
| dc.creator | Kirsch, Werner | |
| dc.creator | Warzel, Simone | |
| dc.date | 2003-10-17 | |
| dc.date | 2004-02-25 | |
| dc.date.accessioned | 2026-07-07T04:30:39Z | |
| dc.date.available | 2026-07-07T04:30:39Z | |
| dc.description | We investigate Lifshits-tail behaviour of the integrated density of states for a wide class of Schrödinger operators with positive random potentials. The setting includes alloy-type and Poissonian random potentials. The considered (single-site) impurity potentials $f: \mathbbm{R}^d \to [0, \infty[ $ decay at infinity in an anisotropic way, for example, $f(x_1,x_2)\sim (|x_1|^{α_1}+|x_2|^{α_2})^{-1}$ as $ |(x_1,x_2)| \to \infty $. As is expected from the isotropic situation, there is a so-called quantum regime with Lifshits exponent $ d/2 $ if both $α_1$ and $α_2$ are big enough, and there is a so-called classical regime with Lifshits exponent depending on $α_1$ and $α_2$ if both are small. In addition to this we find two new regimes where the Lifshits exponent exhibits a mixture of quantum and classical behaviour. Moreover, the transition lines between these regimes depend in a nontrivial way on $ α_1$ and $α_2$ simultaneously. | |
| dc.description | Revised and generalized version | |
| dc.identifier | https://arxiv.org/abs/math-ph/0310033 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0310033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57536 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B44; 82D30; 60K40 | |
| dc.title | Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime | |
| dc.type | text |