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arXiv · 1705.04772

Lifshits tails for randomly twisted quantum waveguides

Werner Kirsch·David Krejcirik·Georgi Raikov
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Abstract

We consider the Dirichlet Laplacian $H_\gamma$ on a 3D twisted waveguide with random Anderson-type twisting $\gamma$. We introduce the integrated density of states $N_\gamma$ for the operator $H_\gamma$, and investigate the Lifshits tails of $N_\gamma$, i.e. the asymptotic behavior of $N_\gamma(E)$ as $E \downarrow \inf {\rm supp}\, dN_\gamma$. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.

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BibTeXRIS

Werner Kirsch, David Krejcirik, Georgi Raikov. 2017-05-12. Lifshits tails for randomly twisted quantum waveguides. https://doi.org/10.1007/s10955-018-2001-5

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