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

Alexander Fedotov (1) , Frédéric Klopp (2)

1 Department of Mathematical Physics - Department of Mathematical Physics
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: quasi periodic Schrödinger equation; pure point spectrum; absolutely continuous spectrum; resonant tunneling; level repulsion

Domaines: Physique mathématique [math-ph]

Alexander Fedotov, Frédéric Klopp. Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators. 2005. ⟨hal-00004248⟩