Inverse problems for Aharonov–Bohm rings

Abstract

AbstractThe inverse problem for Schrödinger operators on metric graphs is investigated in the presence of magnetic field. Graphs without loops and with Euler characteristic zero are considered. It is shown that the knowledge of the Titchmarsh–Weyl matrix function (Dirichlet-to-Neumann map) for just two values of the magnetic field allows one to reconstruct the graph and potential on it provided a certain additional no-resonance condition is satisfied.