We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 - epsilon, where epsilon > 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(root epsilon). We will present a sufficient condition for the existence of a weakly coupled bound state below pi(2), the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when epsilon -> 0(+). RI Cardone, Giuseppe/I-2998-2012 OI Cardone, Giuseppe/0000-0002-5050-8908
BOUND STATES OF A CONVERGING QUANTUM WAVEGUIDE / Cardone, G; Nazarov, Sa; Ruotsalainen, K.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 47:1(2013), pp. 305-315. [10.1051/m2an/2012033]
BOUND STATES OF A CONVERGING QUANTUM WAVEGUIDE
Cardone G
;
2013
Abstract
We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 - epsilon, where epsilon > 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(root epsilon). We will present a sufficient condition for the existence of a weakly coupled bound state below pi(2), the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when epsilon -> 0(+). RI Cardone, Giuseppe/I-2998-2012 OI Cardone, Giuseppe/0000-0002-5050-8908File | Dimensione | Formato | |
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