We study the inverse scattering for Schrödinger 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).
CITATION STYLE
Ando, K., Isozaki, H., & Morioka, H. (2018). Inverse Scattering for Schrödinger Operators on Perturbed Lattices. Annales Henri Poincare, 19(11), 3397–3455. https://doi.org/10.1007/s00023-018-0721-3
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