Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

preprint2005arXivOpen access

Abstract

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.

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