Spectral analysis of metamaterials in curved manifolds

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00379299" target="_blank" >RIV/68407700:21340/25:00379299 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1088/1751-8121/ad9dc5" target="_blank" >https://doi.org/10.1088/1751-8121/ad9dc5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/ad9dc5" target="_blank" >10.1088/1751-8121/ad9dc5</a>

Result language

angličtina

Original language name

Spectral analysis of metamaterials in curved manifolds

Original language description

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 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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Volume of the periodical

58

Issue of the periodical within the volume

2

Country of publishing house

GB - UNITED KINGDOM

Number of pages

32

Pages from-to

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UT code for WoS article

001380298500001

EID of the result in the Scopus database

2-s2.0-85219583117