Quantum waveguides with corners

Dauge, Monique, Lafranche, Yvon, and Raymond, Nicolas. Denis Poisson, Fédération, and Trélat, E., eds. " Quantum waveguides with corners ." ESAIM: Proceedings 35 (2012): 14-45. <http://eudml.org/doc/251242>.

@article{Dauge2012,
abstract = {The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, there are bound states below the free energy band. There are a finite number of them, depending on the opening. This number tends to infinity as the opening tends to 0 (sharply bent V). In this situation, the eigenfunctions concentrate and become self-similar. In contrast, when the opening gets large (almost flat V), the eigenfunctions spread and enjoy a different self-similar structure. We explain all these facts and illustrate them by numerical simulations.},
author = {Dauge, Monique, Lafranche, Yvon, Raymond, Nicolas},
editor = {Denis Poisson, Fédération, Trélat, E.},
journal = {ESAIM: Proceedings},
language = {eng},
month = {4},
pages = {14-45},
publisher = {EDP Sciences},
title = { Quantum waveguides with corners },
url = {http://eudml.org/doc/251242},
volume = {35},
year = {2012},
}

TY - JOUR
AU - Dauge, Monique
AU - Lafranche, Yvon
AU - Raymond, Nicolas
AU - Denis Poisson, Fédération
AU - Trélat, E.
TI - Quantum waveguides with corners
JO - ESAIM: Proceedings
DA - 2012/4//
PB - EDP Sciences
VL - 35
SP - 14
EP - 45
AB - The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, there are bound states below the free energy band. There are a finite number of them, depending on the opening. This number tends to infinity as the opening tends to 0 (sharply bent V). In this situation, the eigenfunctions concentrate and become self-similar. In contrast, when the opening gets large (almost flat V), the eigenfunctions spread and enjoy a different self-similar structure. We explain all these facts and illustrate them by numerical simulations.
LA - eng
UR - http://eudml.org/doc/251242
ER -