A regular version of Smilansky model

Journal Article · Tue Apr 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4870602· OSTI ID:22250670

Barseghyan, Diana ^[1]; Exner, Pavel ^[2]

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1. Fachbereich Mathematik, Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen (Germany)
2. Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic)

We discuss a modification of Smilansky model in which a singular potential “channel” is replaced by a regular, below unbounded potential which shrinks as it becomes deeper. We demonstrate that, similarly to the original model, such a system exhibits a spectral transition with respect to the coupling constant, and determine the critical value above which a new spectral branch opens. The result is generalized to situations with multiple potential “channels.”.

• OSTI ID: 22250670
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
COUPLING CONSTANTS
EIGENVALUES
POTENTIALS