Date(s) : 27/02/2019
10 h 00 min - 11 h 00 min
We consider the forward and inverse scattering problems on the hexagonal lattice. A physically important example is the graphen, for which there are two closely related mathematical models. The first one (the discrete model or the vertex model) deals with the propagation of waves restricted on vertices, and the second one (the quantum graph or the edge model) describes the waves governed by the 1- dimensional Schroedinger equation on the edges. Our main aim is to solve the inverse scattering problems. Assuming that perturbations are confined to a finite part of the graph, for the vertex mode, the S-matrix determines
(1) the potential,
(2) the convex hull of defects of the lattice,
(3) the graph structure as a planar graph.
For the edge model the S-matrix determines
(4) the symmetric potentials on all edges.
This is a joint work with K. Ando, E. Korotyaev and H. Morioka.