Mathematics – Numerical Analysis
Scientific paper
2011-12-19
Mathematics
Numerical Analysis
Scientific paper
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.
Dauge Monique
Lafranche Yvon
Raymond Nicolas
No associations
LandOfFree
Quantum waveguides with corners does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum waveguides with corners, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum waveguides with corners will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-210260