Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.10108 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Negative-index metamaterials possess a negative refractive index and thus present an interesting substance for designing uncommon optical effects such as invisibility cloaking. This paper deals with operators encountered in an operator-theoretic description of metamaterials. First, we introduce an indefinite Laplacian and consider it on a compact tubular neighbourhood in constantly curved compact two-dimensional Riemannian ambient manifolds, with Euclidean rectangle in $\mathbb{R}^2$ being present as a special case. As this operator is not semi-bounded, standard form-theoretic methods cannot be applied. We show that this operator is (essentially) self-adjoint via separation of variables and find its spectral characteristics. We also provide a new method for obtaining alternative definition of the self-adjoint operator in non-critical case via a generalized form representation theorem. The main motivation is existence of essential spectrum in bounded domains.