等离子体共振的量子遍历性和局域化
Quantum ergodicity and localization of plasmon resonances
摘要：
我们关心的是表面等离子体共振（SPR）的几何性质。SPR是在平行于负介电常数/电介质材料界面的方向上传播的非辐射电磁表面波。SPR振荡对材料界面非常敏感。然而，我们表明，SPR振荡渐近局部化的地方，在一定意义上的曲率的高幅度。我们的工作利用了由Shnirelman，Zelditch，Colin de Verdière和Helffer-Martinez-Robert首先导出的量子化和量子遍历性的海森堡图像，以及Neumann-Poincaré算子的某些新的和更一般的遍历性质来分析SPR场，这对谱理论和位势论是独立的兴趣。
英文摘要：
We are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative permittivity/dielectric material interface. It is known that the SPR oscillation is very sensitive to the material interface. However, we show that the SPR oscillation asymptotically localizes at places with high magnitude of curvature in a certain sense. Our work leverages the Heisenberg picture of quantization and quantum ergodicity first derived by Shnirelman, Zelditch, Colin de Verdière and Helffer-Martinez-Robert, as well as certain novel and more general ergodic properties of the Neumann-Poincaré operator to analyze the SPR field, which are of independent interest to the spectral theory and the potential theory.
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