In recent years the study of the Dirac operator on metric graphs has generated a growing interest. It has been widely used for modeling electronic properties of graphene, propagation of electromagnetic waves in graphene-like photonic crystals, ultracold matter in optical lattices and some other physical processes.
In this talk, we consider the dynamic inverse problem for the one-dimensional Dirac system on finite metric tree graphs. The main goal is to recover the topology (connectivity) of a tree, lengths of edges, and a matrix potential function on each edge. We use the dynamic response
operator as inverse data. In addition, we present a new dynamic algorithm to solve the forward problem for the 1-D Dirac system on general finite metric graphs. The talk is based on joint work with Sergei Avdonin and Nina Avdonina.