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Bound states of a converging quantum waveguide

Published online by Cambridge University Press:  23 November 2012

Giuseppe Cardone ,
Sergei A. Nazarov  and
Keijo Ruotsalainen
Giuseppe Cardone
Affiliation:
University of Sannio - Department of Engineering, Piazza Roma, 21, 84100 Benevento, Italy. giuseppe.cardone@unisannio.it
Sergei A. Nazarov
Affiliation:
Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178 St. Petersburg, Russia; srgnazarov@yahoo.co.uk
Keijo Ruotsalainen
Affiliation:
University of Oulu - Department of Electrical Engineering, P.O. Box 4500, 90014 Oulu, Finland; keijo.ruotsalainen@ee.oulu.fi
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Abstract

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

Keywords

Quantum waveguidespectrumasymptotics
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 1 , January 2013 , pp. 305 - 315
Copyright
© EDP Sciences, SMAI, 2012

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