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

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

2005-02-13

arxiv.org/abs/math-ph/0502039v1

Physics

Mathematical Physics

Scientific paper

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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