Singular Continuous Spectrum of rotationally symmetric Dirac operators - Singul\"arstetiges Spektrum kugelsymmetrischer Diracoperatoren

Abstract

The aim of this paper is to construct an explicit potential for the Dirac operator that has purely singular continuous spectrum. The characteristic trait of this potential is that it consists of bumps whose distance is growing rapidly. This allows the particle to depart from the origin arbitrarily far. But the overall effect of the bumps will always lead the particle back to the origin.