On the dense point and absolutely continuous spectrum for Hamiltonians with concentric $\delta$ shells

Abstract

We consider Schrödinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum covers a halfline determined by the appropriate one-dimensional comparison operator; it is dense pure point in the gaps of the latter. If the interaction is radially periodic, there are absolutely continuous bands; in contrast to the regular case the measure of the p.p. segments does not vanish in the high-energy limit.

LaTeX 2e, 12 pages

Cited by in corpus (5)

• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces
• On Self-adjoint extensions and symmetries in Quantum Mechanics
• Quasiperiodic surface Maryland models on quantum graphs
• Aharonov and Bohm vs. Welsh eigenvalues
• 2D Schrödinger operators with singular potentials concentrated near curves