Frank Kleespies, Peter Stollmann
Lifshitz Asymptotics and Localization for Random Quantum Waveguides
(60K, LaTeX2e)

ABSTRACT.  We investigate a family of Dirichlet Laplacians on randomly dented or
bulged strips in $\mathbb{R}^2$; for this random quantum waveguide
model, dense point spectrum with exponentially localized eigenfunctions
near its fluctuation boundary at the bottom of the spectrum and Lifshitz
asymptotics of the integrated density of states are established. For
this purpose, multi-scale analysis in the quite abstract form of
\cite{SLN} is applied, and domain perturbations of the Laplacian are studied.