Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension

dc.creatorKostrykin, Vadim
dc.creatorSchrader, Robert
dc.date2000-05-15
dc.date.accessioned2026-07-07T04:27:48Z
dc.date.available2026-07-07T04:27:48Z
dc.descriptionIn 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.description9 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0005017
dc.identifierhttp://arxiv.org/abs/math-ph/0005017
dc.identifierJ. Phys. A: Math. Gen. 33 (2000) 8231 - 8240
dc.identifierdoi:10.1088/0305-4470/33/46/306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56555
dc.subjectMathematical Physics
dc.subject(2000 Revision) 82B44; 34F05; 60H25
dc.titleGlobal Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension
dc.typetext

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