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Title: A regular version of Smilansky model

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.”.
Authors:
 [1] ;  [2] ;  [3]
  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)
  3. (Czech Republic)
Publication Date:
OSTI Identifier:
22250670
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY-VALUE PROBLEMS; COUPLING CONSTANTS; EIGENVALUES; POTENTIALS