Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators
نویسنده
چکیده
In this paper, we consider one dimensional adiabatic quasi-periodic Schrödinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion. Résumé. Dans cet article, nous étudions une famille d’opérateurs quasi-périodiques adiabatiques dans un cas d’effet tunnel résonant fort. Nous voyons l’apparition d’un phénomène de répulsion de niveaux fort qui est relié au type spectral local de l’opérateur : plus le spectre est singulier, plus la répulsion est faible.
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