Inverse scattering on the quantum graph for graphene

TL;DR

This paper demonstrates that the S-matrix for all energies in a specific spectrum region uniquely determines the compactly supported, symmetric potentials on a quantum graph modeling graphene's hexagonal lattice.

Contribution

It establishes a uniqueness result for inverse scattering on a quantum graph representing graphene, linking the S-matrix to potential recovery.

Findings

S-matrix over an energy set determines potentials

Results apply to symmetric, compactly supported potentials

Focus on quantum graphs modeling 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.