Topics in Analysis on Non-Compact Manifolds

Northeastern University, Boston MA

Investigators

Abstract

Information about DMS-0107796 for FastLane website. Principal investigator: Mikhail Shubin. Abstract. It is planned to obtain necessary and sufficient conditions, as well as explicit necessary and explicit sufficient conditions, for the discreteness of spectrum of magnetic Schroedinger operators on Euclidean space and on Riemannian manifods with geometric restrictions. Presumably the conditions will be given in terms of separation of fields and effective potentials. They will use Wiener capacity and its generalization - magnetic capacity. Physically we are looking for conditions when electrons display a discrete spectrum and are confined into bounded domains for any fixed value of their energy, when such a behavior of electrons results from a joint action of electric and magnetic fields.