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arXiv · 2202.00944

Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph

Emilia Blåsten·Pavel Exner·Hiroshi Isozaki·Matti Lassas·Jinpeng Lu
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Abstract

We consider the inverse scattering problems for two types of Schr\"odinger 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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Emilia Blåsten, Pavel Exner, Hiroshi Isozaki, Matti Lassas, Jinpeng Lu. 2022-02-02. Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph. https://arxiv.org/abs/2202.00944

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