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Open Quantum Systems Decoherence
Quantum Simulation
On the dense point and absolutely continuous spectrum for Hamiltonians with concentric δ shells
arXiv
Authors: Pavel Exner, Martin Fraas
Year
2007
Paper ID
50350
Status
Preprint
Abstract Read
~2 min
Abstract Words
88
Citations
N/A
Abstract
We consider Schrödinger operator in dimension dge 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.
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- We consider Schrödinger operator in dimension dge 2 with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel...
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