Inverse Scattering for Schrödinger Operators on Perturbed Lattices

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 g...

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Bibliographic Details
Published in:Annales Henri Poincaré 2018-11, Vol.19 (11), p.3397-3455
Main Authors: Ando, Kazunori, Isozaki, Hiroshi, Morioka, Hisashi
Format: Article
Language:English
Subjects:
Boundary value problems
Classical and Quantum Gravitation
Dirichlet problem
Dynamical Systems and Ergodic Theory
Elementary Particles
Graphene
Inverse scattering
Lattices
Mathematical and Computational Physics
Mathematical Methods in Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
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Summary: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).
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-018-0721-3