---
abstract: |
    In this paper, we consider one dimensional adiabatic quasi-periodic Schr[ö]{}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.

    .5cm

    <span style="font-variant:small-caps;">R[é]{}sum[é]{}.</span> Dans cet article, nous [é]{}tudions une famille d’op[é]{}rateurs quasi-p[é]{}riodiques adiabatiques dans un cas d’effet tunnel r[é]{}sonant fort. Nous voyons l’apparition d’un ph[é]{}nom[è]{}ne de r[é]{}pulsion de niveaux fort qui est reli[é]{} au type spectral local de l’op[é]{}rateur : plus le spectre est singulier, plus la r[é]{}pulsion est faible.
address:
- 'Department of Mathematical Physics, St Petersburg State University, 1, Ulianovskaja, 198904 St Petersburg-Petrodvorets, Russia'
- 'LAGA, Institut Galil[é]{}e, U.M.R. 7539 C.N.R.S, Universit[é]{} Paris-Nord, Avenue J.-B. Cl[é]{}ment, F-93430 Villetaneuse, France'
author:
- Alexander Fedotov
- 'Fr[é]{}d[é]{}ric Klopp'
title: 'Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic [Schr[ö]{}dinger]{} operators'
---

[10]{}

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