Inverse scattering on the quantum graph for graphene

Abstract

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set in the continuous spectrum determines the potentials.

Many parts of this paper, especially the part dealing with the the forward problem, can be generalized to more general lattices, which can be seen in arXiv:1911.05233

References in corpus (4)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Spectral Properties of Schrödinger Operators on Perturbed Lattices
• Scattering on periodic metric graphs
• Inverse scattering on the quantum graph -- Edge model for graphen