Metamaterials and Cesàro convergence
In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Cesàro convergence. Then, we also show the analytical continuation of permittivity and permeability to the complex plane in terms of the Riemann zeta (ζ) function...
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AIP Publishing LLC
2020-04-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.5144629 |
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doaj-2a2b6dd0bcca438db3ba215475f3aeba2020-11-25T02:20:39ZengAIP Publishing LLCAIP Advances2158-32262020-04-01104045127045127-610.1063/1.5144629Metamaterials and Cesàro convergenceYuganand Nellambakam0K. V. S. Shiv Chaitanya1Department of Physics, BITS Pilani, Hyderabad Campus, Jawahar Nagar, Shamirpet Mandal, Hyderabad 500 078, IndiaDepartment of Physics, BITS Pilani, Hyderabad Campus, Jawahar Nagar, Shamirpet Mandal, Hyderabad 500 078, IndiaIn this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Cesàro convergence. Then, we also show the analytical continuation of permittivity and permeability to the complex plane in terms of the Riemann zeta (ζ) function. The nontrivial zeros on the half-line of the Riemann zeta (ζ) function correspond to permittivity ξe = 0 and permeability ξm = 0. The permittivity ξe = 0 and permeability ξm = 0 in the literature are known as zero index materials.http://dx.doi.org/10.1063/1.5144629 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yuganand Nellambakam K. V. S. Shiv Chaitanya |
| spellingShingle |
Yuganand Nellambakam K. V. S. Shiv Chaitanya Metamaterials and Cesàro convergence AIP Advances |
| author_facet |
Yuganand Nellambakam K. V. S. Shiv Chaitanya |
| author_sort |
Yuganand Nellambakam |
| title |
Metamaterials and Cesàro convergence |
| title_short |
Metamaterials and Cesàro convergence |
| title_full |
Metamaterials and Cesàro convergence |
| title_fullStr |
Metamaterials and Cesàro convergence |
| title_full_unstemmed |
Metamaterials and Cesàro convergence |
| title_sort |
metamaterials and cesàro convergence |
| publisher |
AIP Publishing LLC |
| series |
AIP Advances |
| issn |
2158-3226 |
| publishDate |
2020-04-01 |
| description |
In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Cesàro convergence. Then, we also show the analytical continuation of permittivity and permeability to the complex plane in terms of the Riemann zeta (ζ) function. The nontrivial zeros on the half-line of the Riemann zeta (ζ) function correspond to permittivity ξe = 0 and permeability ξm = 0. The permittivity ξe = 0 and permeability ξm = 0 in the literature are known as zero index materials. |
| url |
http://dx.doi.org/10.1063/1.5144629 |
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AT yuganandnellambakam metamaterialsandcesaroconvergence AT kvsshivchaitanya metamaterialsandcesaroconvergence |
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