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• W4287023473 abstract "The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We firstly study how the capacitance matrix formalism, both when the material parameters are static and modulated, can be posed in a Hamiltonian form. Then, we use this result to compare this formalism to the tight-binding approximation. We prove that the correspondence between the capacitance formulation and the tight-binding approximation holds only in the case of dilute resonators. On the other hand, the tight-binding model is often coupled with a nearest-neighbour approximation, whereby long-range interactions are neglected. Even in the dilute case, we show that long-range interactions between subwavelength resonators are relatively strong and nearest-neighbour approximations are not generally appropriate." @default.
• W4287023473 created "2022-07-25" @default.
• W4287023473 creator A5036607089 @default.
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• W4287023473 date "2021-08-18" @default.
• W4287023473 modified "2023-09-27" @default.
• W4287023473 title "On the validity of the tight-binding method for describing systems of subwavelength resonators" @default.
• W4287023473 doi "https://doi.org/10.48550/arxiv.2108.08223" @default.
• W4287023473 hasPublicationYear "2021" @default.
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