Lifschitz Tails and Localisation for a Class of Schrödinger Operators with Random Breather-type Potential
نویسندگان
چکیده
We derive bounds on the integrated density of states of Schrödinger operators with a random, ergodic potential. The potential depends on a sequence of random variables, not necessarily in a linear way. An example of such a random Schrödinger operator is the breather model, as introduced by Combes, Hislop and Mourre. For these models we show that the the integrated density of states near the bottom of the spectrum behaves according to the so called Lifshitz asymptotics. This enables us to prove localisation in certain energy/disorder regimes.
منابع مشابه
Lifshitz Tails for Generalized Alloy Type Random Schrödinger Operators
We study Lifshitz tails for random Schrödinger operators where the random potential is alloy type in the sense that the single site potentials are independent, identically distributed, but they may have various function forms. We suppose the single site potentials are distributed in a finite set of functions, and we show that under suitable symmetry conditions, they have Lifshitz tail at the bo...
متن کاملLifshitz tails for random perturbations of periodic Schrödinger operators
The present paper is a non-exhaustive review of Lifshitz tails for random perturbations of periodic Schrödinger operators. It is not our goal to review the whole literature on Lifshitz tails; we will concentrate on a single model, the continuous Anderson model.
متن کاملLocalisation for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues∗
We prove a localisation theorem for continuous ergodic Schrödinger operators Hω := H0 + Vω, where the random potential Vω is a nonnegative Anderson-type random perturbation of the periodic operator H0. We consider a lower spectral band edge of σ(H0), say E = 0, at a gap which is preserved by the perturbation Vω. Assuming that all Floquet eigenvalues of H0, which reach the spectral edge 0 as a m...
متن کاملOptimal Wegner Estimates for Random Schrödinger Operators on Metric Graphs
We consider Schrödinger operators with a random potential of alloy type on infinite metric graphs which obey certain uniformity conditions. For single site potentials of fixed sign we prove that the random Schrödinger operator restricted to a finite volume subgraph obeys a Wegner estimate which is linear in the volume and reproduces the modulus of continuity of the single site distribution. Thi...
متن کاملGap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model
We consider a modulated discrete nonlinear Schrödinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a ’forbidden’ gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap – discrete gap and out-gap breathers (DGBs and DOGBs) – are investigated. Their linear stability is studied varying the system pa...
متن کامل