05-366 Hatem NAJAR

The spectrum minimum for random Schr\"odinger operators with indefinite sign potentials (747K, pdf, dvi, ps) Oct 24, 05

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Abstract. This paper sets out to study the spectral minimum for operator belonging to the family of random Schr\"odinger operators of the form $H_{\lambda,\omega}=-\Delta+W_{\text{per}}+\lambda V_{\omega}$, where we suppose that $V_{\omega}$ is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists $\lambda_0>0$ such that for any $\lambda \in [0,\lambda_0]$, the minimum of the spectrum of $H_{\lambda,\omega}$ is obtained by a given realization of the random variables.

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