2D- and 3DMagnetic Schroedinger Operators: Short Loops, Pointwise Spectral Asymptotics and Asymptotics of Dirac Energy

Abstract

We consider 2- and 3-dimensional Schrödinger or generalized Schrödinger-Pauli operators with the non-degenerating magnetic field in the open domain under certain non-degeneracy assumptions we derive pointwise spectral asymptotics. We also consider asymptotics of some related expressions (see below). For all asymptotics loops rather than periodic trajectories play important role.

147 pp, 12 fig