A. Fedotov, F. Klopp
Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr dinger operators
(1196K, Portable document file)

ABSTRACT.  In this paper, we consider one dimensional adiabatic quasi-periodic Schr 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.