Curvature-Induced Bound States In Quantum Waveguides In Two And Three Dimensions (1995)
| Venue: | Math. Phys |
| Citations: | 56 - 8 self |
BibTeX
@ARTICLE{Duclos95curvature-inducedbound,
author = {Pierre Duclos and Pavel Exner},
title = {Curvature-Induced Bound States In Quantum Waveguides In Two And Three Dimensions},
journal = {Math. Phys},
year = {1995},
volume = {7},
pages = {73--102}
}
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Abstract
Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated. It is shown that if the tube is non--straight and its curvature vanishes asymptotically, there is always a bound state below the bottom of the essential spectrum. An upper bound to the number of these bound states in thin tubes is derived. Furthermore, if the tube is only slightly bent, there is just one bound state; we derive its behaviour with respect to the bending angle. Finally, perturbation theory of these eigenvalues in any thin tube with respect to the tube radius is constructed and some open questions are formulated. October 1994 CPT-94/P.3023 anonymous ftp or gopher: cpt.univ-mrs.fr Unit'e Propre de Recherche 7061 1 and PHYMAT, Universit'e de Toulon et du Var, 83130 Lagarde, France duclos@naxos.unice.fr 2 Nuclear Physics Institute, AS CR, 25068 Rez near Prague and Doppler Institute, Czech Technical University, Brehov'a 7, 11519 Prague, Czech Republic exner@uj...
