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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2602.02998 |
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| _version_ | 1866914303678873600 |
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| author | Chen, Bochao Gao, Yixian Liu, Hongyu |
| author_facet | Chen, Bochao Gao, Yixian Liu, Hongyu |
| contents | The Neumann--Poincaré (NP) operator, a fundamental operator in potential theory, has attracted renewed attention for its central role in the analysis of surface plasmon resonances (SPRs). SPRs, characterized by non-radiative electromagnetic waves at material interfaces with opposing permittivities, underpin advanced technologies such as bio-sensing and cloaking devices. While spectral properties of the scalar NP operator and SPR dynamics for scalar waves are well-established, their vectorial counterparts in Maxwell's framework remain poorly understood. This work bridges this gap by introducing a novel symmetrization principle for the matrix-valued Maxwell Neumann--Poincaré (MNP) operator, enabling a spectral decomposition of traces in the $\mathbf{H}(\mathrm{curl},D)$ space--a foundational advance for electromagnetic theory. Building on this framework, we rigorously characterize the quantum-ergodic localization of weak surface plasmon resonances at material boundaries in the full Maxwell system, thereby settling a long-standing question concerning their quantitative description. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02998 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetrization of the Maxwell--Neumann--Poincar'e operator, spectral decomposition in $\mathbf{H}(\mathrm{curl},D)$ traces, and boundary localisation of SPRs Chen, Bochao Gao, Yixian Liu, Hongyu Analysis of PDEs The Neumann--Poincaré (NP) operator, a fundamental operator in potential theory, has attracted renewed attention for its central role in the analysis of surface plasmon resonances (SPRs). SPRs, characterized by non-radiative electromagnetic waves at material interfaces with opposing permittivities, underpin advanced technologies such as bio-sensing and cloaking devices. While spectral properties of the scalar NP operator and SPR dynamics for scalar waves are well-established, their vectorial counterparts in Maxwell's framework remain poorly understood. This work bridges this gap by introducing a novel symmetrization principle for the matrix-valued Maxwell Neumann--Poincaré (MNP) operator, enabling a spectral decomposition of traces in the $\mathbf{H}(\mathrm{curl},D)$ space--a foundational advance for electromagnetic theory. Building on this framework, we rigorously characterize the quantum-ergodic localization of weak surface plasmon resonances at material boundaries in the full Maxwell system, thereby settling a long-standing question concerning their quantitative description. |
| title | Symmetrization of the Maxwell--Neumann--Poincar'e operator, spectral decomposition in $\mathbf{H}(\mathrm{curl},D)$ traces, and boundary localisation of SPRs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.02998 |