Inverse scattering for Schrödinger operators on perturbed lattices

Abstract

We study the inverse scattering for Schr{ö}dinger operators on locally perturbed periodic lattices. We show that the associated scattering matrix is equivalent to the Dirichlet-to-Neumann map for a boundary value problem on a finite part of the graph, and reconstruct scalar potentials as well as the graph structure from the knowledge of the S-matrix. In particular, we give a procedure for probing defects in hexagonal lattices (graphene).

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Cited by in corpus (5)

• Scattering on periodic metric graphs
• Continuum limit for lattice Schrödinger operators
• Spectral and scattering theory for topological crystals perturbed by infinitely many new edges
• Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks
• Gel'fand's inverse problem for the graph Laplacian