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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+.
@article{M2AN_2013__47_1_305_0,
author = {Cardone, Giuseppe and Nazarov, Sergei A. and Ruotsalainen, Keijo},
title = {Bound states of a converging quantum waveguide},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {305--315},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
doi = {10.1051/m2an/2012033},
mrnumber = {2997503},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012033/}
}
TY - JOUR AU - Cardone, Giuseppe AU - Nazarov, Sergei A. AU - Ruotsalainen, Keijo TI - Bound states of a converging quantum waveguide JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 305 EP - 315 VL - 47 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012033/ DO - 10.1051/m2an/2012033 LA - en ID - M2AN_2013__47_1_305_0 ER -
%0 Journal Article %A Cardone, Giuseppe %A Nazarov, Sergei A. %A Ruotsalainen, Keijo %T Bound states of a converging quantum waveguide %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 305-315 %V 47 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012033/ %R 10.1051/m2an/2012033 %G en %F M2AN_2013__47_1_305_0
Cardone, Giuseppe; Nazarov, Sergei A.; Ruotsalainen, Keijo. Bound states of a converging quantum waveguide. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 1, pp. 305-315. doi: 10.1051/m2an/2012033
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