Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension
| dc.creator | Kostrykin, Vadim | |
| dc.creator | Schrader, Robert | |
| dc.date | 2000-05-15 | |
| dc.date.accessioned | 2026-07-07T04:27:48Z | |
| dc.date.available | 2026-07-07T04:27:48Z | |
| dc.description | In this article we prove an upper bound for the Lyapunov exponent $γ(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schrödinger operators in one dimension. These Schrödinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $γ(E)$ and $N(E)-\sqrt{E}/π$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0005017 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0005017 | |
| dc.identifier | J. Phys. A: Math. Gen. 33 (2000) 8231 - 8240 | |
| dc.identifier | doi:10.1088/0305-4470/33/46/306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56555 | |
| dc.subject | Mathematical Physics | |
| dc.subject | (2000 Revision) 82B44; 34F05; 60H25 | |
| dc.title | Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension | |
| dc.type | text |