07-254 O. Safronov

Absolutely continuous spectrum of one random elliptic operator (revised) (159K, pdf) Oct 28, 07

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Abstract. We consider the differential operator $H_0=-\Delta+|x|^{-\varepsilon}(-\Delta_\theta)$ with $\varepsilon>0$. Here $\Delta_\theta$ is the Laplace-Beltrami operator on the unit sphere. We perturb now the operator $H_0$ by a random real valued potential $V=V_\omega$ and prove that the perturbed operator has an absolutely continuous component in the spectrum.

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