Volume 7 (2024)
Blåsten, Emilia; Exner, Pavel; Isozaki, Hiroshi; Lassas, Matti; Lu, Jinpeng
Inverse problems for locally perturbed lattices – Discrete Hamiltonian and quantum graph
Annales Henri Lebesgue, Volume 7 (2024), pp. 267-305.

Metadata

DOI10.5802/ahl.201
Keywords lattice, metric graph, discrete Hamiltonian, S-matrix, inverse porblem

Abstract

We consider the inverse scattering problems for two types of Schrödinger operators on locally perturbed periodic lattices. For the discrete Hamiltonian, the knowledge of the S-matrix for all energies determines the graph structure and the coefficients of the Hamiltonian. For locally perturbed equilateral metric graphs, the knowledge of the S-matrix for all energies determines the graph structure.


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