Spectral and scattering theory for Schrödinger operators on perturbed topological crystals

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 completeness of local wave operators are also proved.

36 pages

References in corpus (3)

• Spectral Properties of Schrödinger Operators on Perturbed Lattices
• Spectral analysis for adjacency operators on graphs
• Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals

Cited by in corpus (7)

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• Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator