Strong resonant tunneling, level repulsion and spectral type for   one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators
  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. 
Alexander Fedotov (Department of Mathematical Physics), Fr\'ed\'eric   Klopp (LAGA)