Inverse scattering on perturbed periodic lattices

Hiroshi Isozaki
(University of Tsukuba )
Analysis Seminar
Thursday, 22 February, 2018, at 16:15-17:00, in Aud. D3 (1531-215)
Abstract:
We consider the inverse scattering problem associated with Schroedinger
operators on perturbed periodic lattices. Our final goal is the
reconstruction of the potential on each vertex or the defect of the
lattice from the scattering matrix. A typical example is the graphen
based on the hexagonal lattice. The main tool is the stationary
scattering theory developed for Schroedinger operators for continuous
models. In particular, micro-local calculus on the torus, elementary
algebraic geometry as well as techniques developed for graph Laplacians
play an effective role to study the Lattice Schroedinger operators,
revealing clear parallelism between them. These ideas are also applied
to the inverse scattering for the metric graph, in which case we
reconstruct the potentials on each edge from the S-matrix.
Contact person: Erik Skibsted