Abstract

We consider the Dirichlet Laplacian Hγ on a 3D twisted waveguide with random Anderson-type twisting γ. We introduce the integrated density of states Nγ for the operator Hγ, and investigate the Lifshits tails of Nγ, i.e. the asymptotic behavior of Nγ(E) as E↓infsuppdNγ. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.