Fr\'ed\'eric Klopp
Internal Lifshits tails for random perturbations of periodic Schr\"odinger
operators
(308K, uuencoded gzipped Postscript)
ABSTRACT. Let $H$ be a $\Gamma$-periodic Schr\"odinger operator acting on $L^2(\Rd)$
and consider the random Schr\"odinger operator $H_\omega=H+V_\omega$ where
$\D V_\omega(x)=\sum_{\gamma\in\Gamma}\omega_\gamma V(x-\gamma)$ (here $V$
is a positive potential and $(\omega_\gamma)_{\gamma\in\Gamma}$ a
collection of positive i.i.d random variables). We prove that, at the edge
of a gap of $H$ that is not filled in for $H_\omega$, the integrated
density of states of $H_\omega$ has a Lifshits tail behaviour if and only
if the integrated density of states of $H$ is non-degenerate.