Inverse scattering on the quantum graph -- Edge model for graphen

TL;DR

This paper demonstrates that the S-matrix for a quantum graph with a hexagonal lattice uniquely determines the edge potentials when they are compactly supported, for all energies in an open spectral set.

Contribution

It introduces an inverse scattering method for quantum graphs on a hexagonal lattice, establishing uniqueness of potential recovery from the S-matrix.

Findings

S-matrix determines edge potentials uniquely

Results apply to all energies in an open spectral set

Focus on quantum graphs with hexagonal lattice structure

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, we show that the S-matrix for all energies in any open set in the continuous spectrum determines the potentials.