A nonlinear eigenvalue problem arising in a nanostructured quantum dot
Mathematical Physics
2015-06-19 v1 Analysis of PDEs
math.MP
Optimization and Control
Abstract
In this paper we investigate a minimization problem related to the principal eigenvalue of the -wave Schr\"{o}dinger operator. The operator depends nonlinearly on the eigenparameter. We prove the existence of a solution for the optimization problem and the uniqueness will be addressed when the domain is a ball. The optimized solution can be applied to design new electronic and photonic devices based on the quantum dots.
Cite
@article{arxiv.1403.7762,
title = {A nonlinear eigenvalue problem arising in a nanostructured quantum dot},
author = {Abbasali Mohammadi and Fariba Bahrami},
journal= {arXiv preprint arXiv:1403.7762},
year = {2015}
}