论文标题
等离子共振的量子性牙齿和定位
Quantum ergodicity and localization of plasmon resonances
论文作者
论文摘要
我们关注表面等离子体共振（SPR）的几何特性。 SPR是一种非辐射电磁表面波，在平行于负介电常数/介电材料界面的方向上传播。众所周知，SPR振荡对材料界面非常敏感。但是，我们表明，SPR振荡在某种意义上渐近地定位于具有曲率高的地方。我们的工作利用了Shnirelman，Zelditch，Colin deVerdière和Helfer-Martinez-Robert以及某些新颖和更一般的诸如诺伊曼 - 庞卡尔运营商的诺伊曼 - 庞塞尔运营商的新颖性和更一般的厄戈迪克特性，并利用了Shnirelman，Zelditch，Zelditch，Colin deVerdière和Helfer-Martinez-Robert的最初得出的Heisenberg图片。
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.
