近日，法国巴黎萨克雷大学的Thorsten Emig及其研究团队取得一项新进展。他们实现了介质楔卡西米尔-波尔德相互作用的表面散射展开。相关研究成果已于2024年12月11日在国际知名学术期刊《物理评论A》上发表。

据悉，介质楔的电磁散射振幅没有已知的闭合形式。这使得计算可极化粒子与介质楔之间的，卡西米尔-波尔德（Casimir-Polder，CP）相互作用变得具有挑战性。这种几何形状是研究边缘对涨落诱导相互作用影响的原型，因此，针对这个问题采用新方法非常重要。

利用最近开发的多重散射展开方法[Emig和Bimonte, Phys. Rev. Lett. 130, 200401 (2023)]，该研究团队实现了对该展开的无基数值评估，以获得楔形结构在广泛介电常数范围内卡西米尔-波尔德（CP）势的精确估计。一个显著的发现是，具有平滑边缘的介质楔的CP势与由完美电导体制成的尖楔的势密切相关。后者已知确切的势，使得这种关系在实际应用中特别有用。

附：英文原文

Title: Surface scattering expansion for the Casimir-Polder interaction of a dielectric wedge

Author: Thorsten Emig

Issue&Volume: 2024/12/11

Abstract: The electromagnetic scattering amplitude of a dielectric wedge is not known in closed form. This makes the computation of the Casimir-Polder (CP) interaction between a polarizable particle and a dielectric wedge challenging. This geometry is a prototype for the effect of edges on fluctuation-induced interactions, and hence, it is important to employ new methods for this problem. Using a recently developed multiple-scattering expansion [Emig and Bimonte, Phys. Rev. Lett. 130, 200401 (2023)], here, we implement a basis-free numerical evaluation of this expansion to obtain precise estimates of the CP potential for a wedge over a wide range of dielectric constants. A remarkable finding is that the CP potential for a dielectric wedge with a smoothed edge is closely related to the potential of a sharp wedge made of a perfect electric conductor. The latter potential is known exactly, making this relation particularly useful in practice.

DOI: 10.1103/PhysRevA.110.062809

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062809