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Open Quantum Systems Decoherence Quantum Simulation

Aharonov and Bohm vs. Welsh eigenvalues

arXiv
Authors: Pavel Exner, Sylwia Kondej

Year

2017

Paper ID

24526

Status

Preprint

Abstract Read

~2 min

Abstract Words

107

Citations

N/A

Abstract

We consider a class of two-dimensional Schrödinger operator with a singular interaction of the δ type and a fixed strength β supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an Aharonov-Bohm flux αin \[0,frac12\] in the center. It is shown that if βne 0, there is a critical value αcrit in\(0,frac12\) such that the discrete spectrum has an accumulation point when α<αcrit, while for αgeαcrit the number of eigenvalues is at most finite, in particular, the discrete spectrum is empty for any fixed αin \(0,frac12\) and |β| small enough.

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  • We consider a class of two-dimensional Schrödinger operator with a singular interaction of the δ type and a fixed strength β supported by an infinite family of concentric...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1712.04897 [2] arXiv https://arxiv.org/abs/1712.04897 [3] Publisher https://arxiv.org/abs/1712.04897

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