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

Abstract

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.

References in corpus (4)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• Geometric tools of the adiabatic complex WKB method
• On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line
• Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

Cited by in corpus (2)

• Bulk Universality and Clock Spacing of Zeros for Ergodic Jacobi Matrices with A.C. Spectrum
• Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators