The spectrum minimum for random Schrödinger operators with indefinite sign potentials

Details The spectrum minimum for random Schrödinger operators with indefinite sign potentials The spectrum minimum for random Schrödinger operators with indefinite sign potentials

2005-10-25

arxiv.org/abs/math/0510522v1

Mathematics

Spectral Theory

Scientific paper

10.1063/1.2162825

This paper sets out to study the spectral minimum for operator belonging to the family of random Schr\"{o}dinger 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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