Lifshits tails for randomly twisted quantum waveguides

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 $E\downarrow \inf \mathrm{supp}d{N}_{\gamma }$. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.

18 pages, introduction modified, typos corrected

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• Location of the essential spectrum in curved quantum layers
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Cited by in corpus (1)

• Lifshits Tails for Squared Potentials