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Annales Henri Poincaré

, Volume 19, Issue 11, pp 3397–3455 | Cite as

Inverse Scattering for Schrödinger Operators on Perturbed Lattices

  • Kazunori Ando
  • Hiroshi IsozakiEmail author
  • Hisashi Morioka
Article

Abstract

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).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Kazunori Ando
    • 1
  • Hiroshi Isozaki
    • 2
    Email author
  • Hisashi Morioka
    • 3
  1. 1.Department of Electrical and Electronic Engineering and Computer ScienceEhime UniversityMatsuyamaJapan
  2. 2.Professor EmeritusUniversity of TsukubaTsukubaJapan
  3. 3.Faculty of Science and EngineeringDoshisha UniversityKyotanabeJapan

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