Bound states of a converging quantum waveguide

Giuseppe Cardone; Sergei A. Nazarov; Keijo Ruotsalainen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 1, page 305-315
  • ISSN: 0764-583X

Abstract

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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+.

How to cite

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Cardone, Giuseppe, Nazarov, Sergei A., and Ruotsalainen, Keijo. "Bound states of a converging quantum waveguide." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.1 (2013): 305-315. <http://eudml.org/doc/273154>.

@article{Cardone2013,
abstract = {We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 − ε, where ε &gt; 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+.},
author = {Cardone, Giuseppe, Nazarov, Sergei A., Ruotsalainen, Keijo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quantum waveguide; spectrum; asymptotics},
language = {eng},
number = {1},
pages = {305-315},
publisher = {EDP-Sciences},
title = {Bound states of a converging quantum waveguide},
url = {http://eudml.org/doc/273154},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 1
SP - 305
EP - 315
AB - We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 − ε, where ε &gt; 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+.
LA - eng
KW - quantum waveguide; spectrum; asymptotics
UR - http://eudml.org/doc/273154
ER -

References

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