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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.



Author: Pavel Exner, Martin Fraas

Source: https://arxiv.org/







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