A nonlinear eigenvalue problem arising in a nanostructured quantum dot. (English) Zbl 1448.81331
Summary: In this paper we investigate a minimization problem related to the principal eigenvalue of the \(s\)-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.
MSC:
| 81Q37 | Quantum dots, waveguides, ratchets, etc. |
| 82D80 | Statistical mechanics of nanostructures and nanoparticles |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
| 49K20 | Optimality conditions for problems involving partial differential equations |
Keywords:
\(s\)-wave Schrödinger operator; optimization problems; nanostructured quantum dots; rearrangementReferences:
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