paper

A nonlinear eigenvalue problem arising in a nanostructured quantum dot

arXiv:1403.7762 · doi:10.1016/j.cnsns.2013.11.017

Abstract

In this paper we investigate a minimization problem related to the principal eigenvalue of the -wave Schrödinger 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.

A nonlinear eigenvalue problem arising in a nanostructured quantum dot · wovepaper