Inverse problems for quantum graph associated with square and hexagonal lattices

TL;DR

This paper addresses inverse problems related to quantum graphs on square and hexagonal lattices, focusing on reconstructing graph properties from boundary measurements and scattering data.

Contribution

It introduces methods to solve inverse boundary value and scattering problems for quantum graphs on square and hexagonal lattices, extending inverse problem techniques to these lattice structures.

Findings

Successfully reconstructs quantum graph properties from D-N maps.

Solves inverse scattering problems from S-matrix data.

Extends inverse problem methods to lattice-based quantum graphs.

Abstract

We solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from the S-matrix for a locally perturbed square lattice and a hexagonal lattice.