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Bound states of a converging quantum waveguide

Published online by Cambridge University Press:  23 November 2012

Giuseppe Cardone
Affiliation:
University of Sannio - Department of Engineering, Piazza Roma, 21, 84100 Benevento, Italy. [email protected]
Sergei A. Nazarov
Affiliation:
Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178 St. Petersburg, Russia; [email protected]
Keijo Ruotsalainen
Affiliation:
University of Oulu - Department of Electrical Engineering, P.O. Box 4500, 90014 Oulu, Finland; [email protected]
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Abstract

We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1and 1 − ε, where ε > 0 is a small real parameter,i.e. the waveguide is gently converging. The width of the junction zonefor the semi-strips is 1 + O(√ε). We will present a sufficient condition for the existence of a weaklycoupled bound state below π2, the lower bound of thecontinuous spectrum. This eigenvalue in the discrete spectrum is unique and itsasymptotics is constructed and justified whenε → 0+.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2012

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