Vu Hoang (Karlsruhe)

Title: Nonexistence of bound states for a periodic waveguide problem

(Joint work with Maria Radosz)

Abstract:
I consider a two-dimensional periodic medium, which is perturbed
by a line defect (a waveguide). In this situation, one expects that the
associated partially periodic self-adjoint operator has no bound states
on the whole space. This fact is surprisingly hard to prove and the
the result was achieved only recently.

In this talk, I give an introduction to the analysis of periodic elliptic
operators and discuss the nonexistence of bound states based on
a classical argument by L. Thomas. Finally, I give a few details of
our proof.