# On the dense point and absolutely continuous spectrum for Hamiltonians with concentric \$δ\$ shells - Mathematical Physics

On the dense point and absolutely continuous spectrum for Hamiltonians with concentric \$δ\$ shells - Mathematical Physics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We consider Schr\-odinger operator in dimension \$d\ge 2\$ with a singularinteraction supported by an infinite family of concentric spheres, analogous toa system studied by Hempel and coauthors for regular potentials. The essentialspectrum covers a halfline determined by the appropriate one-dimensionalcomparison operator; it is dense pure point in the gaps of the latter. If theinteraction is radially periodic, there are absolutely continuous bands; incontrast to the regular case the measure of the p.p. segments does not vanishin the high-energy limit.

Autor: Pavel Exner, Martin Fraas

Fuente: https://arxiv.org/