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Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators

Alexander Fedotov·Frédéric Klopp
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Abstract

In this paper, we consider one dimensional adiabatic quasi-periodic Schr\"{o}dinger 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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Alexander Fedotov, Frédéric Klopp. 2005-02-13. Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators. https://doi.org/10.1007/3-540-34273-7_28

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