## The width of resonances for slowly varying perturbations of one-dimensional periodic Schrödinger operators.(English. French summary)Zbl 1118.34082

Author’s abstract: We report on results about the width of the resonances for a slowly varying perturbation of a periodic operator. The study takes place in dimension one. The perturbation is assumed to be analytic and local in the sense that it tends to a constant at$$+\infty$$ and $$-\infty$$; these constants may differ. Modulo an assumption on the relative position of the range of the local perturbation with respect to the spectrum, of the background periodic operator, we show that the width of the resonances is essentially given by a tunneling effect in a suitable phase space.

### MSC:

 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34E05 Asymptotic expansions of solutions to ordinary differential equations 34L05 General spectral theory of ordinary differential operators

### Keywords:

complex WKB method
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