97-81 Fr\'ed\'eric Klopp

Internal Lifshits tails for random perturbations of periodic Schr\"odinger operators (308K, uuencoded gzipped Postscript) Feb 17, 97

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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.

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