We study the inverse scattering for Schrodinger operators on locally perturbed periodic lattices. We show that the associated scattering matrix is equivalent to the Dirichlet-to-Neumann map for a boundary value problem on a finite part of the graph, and reconstruct scalar potentials as well as the graph structure from the knowledge of the S-matrix. In particular, we give a procedure for probing defects in hexagonal lattices (graphene).
Introduction. Operateurs lineaires associes a un graphe. Resultats fondamentaux. Rayon spectral, fonctions generatrices de marche et mesures spectrales. Croissance et nombre isoperimetrique d'un graphe. Fonctions propres positives. Graphes de groupes, arbres et graphes reguliers en distance. Quelques remarques sur les applications en chimie et en physique