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Spectral and scattering theory for Schrödinger operators on perturbed topological crystals

Univ. Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Blvd. du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France

E-mail Address: parra@math.univ-lyon1.fr

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and

S. Richard

Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan

E-mail Address: richard@math.nagoya-u.ac.jp

On leave of absence from Univ. Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Blvd. du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France.

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https://doi.org/10.1142/S0129055X18500095Cited by:14 (Source: Crossref)

Abstract

In this paper, we investigate the spectral and the scattering theory of Schrödinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or a long-range function, or a short-range type modification of the measure defined on the vertices and on the edges of the graph. Mourre theory is used for describing the nature of the spectrum of the underlying operators. For short-range perturbations, existence and asymptotic completeness of local wave operators are also proved.

Keywords:

AMSC: 47A10, 05C63, 35R02

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