Emily Blasten, Pavel Exner, Hiroshi Isozaki, Matti Lassas, Jinpeng Lu
Inverse problems for locally perturbed lattices - Discrete Hamiltonian and quantum graph
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ABSTRACT.  We consider the inverse scattering problems for two types of Schr dinger 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.