Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder
Spectral Methods in Mathematical Physics
19 February 15:30 - 16:30
Sara Maad Sasane - Lund University
Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this talk, I will describe a perturbation problem for embedded eigenvalues for a magnetic Schrödinger operator, when the underlying domain is a cylinder. The magnetic potential is has an algebraic decay rate as the unbounded variable of the cylinder tends to infinity in both directions.
We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension. This is joint work with Ari Laptev.
University of Zurich, UZH