We consider the mathematical problem of electromagnetic wave scattering by a plasmonic dimer composed of noble metal nanoparticles with sizes less than tens of nanometers. To develop mathematical models, the efficient discrete sources method is used, which makes it possible to take all peculiar features of such systems into account, including the shapes of particles and the effects of spatial dispersion, which are also known as nonlocal effects. It is shown that in the case of external fields that are independent of the azimuthal harmonics, it is possible to approximate the problem solution using the system of vertical dipoles on the axis of symmetry of the particle. Based on the hybrid scheme of the discrete sources method, the problem of excitation of a dimer by the field of a point charge in uniform straight motion in a homogeneous space is first solved.

中文翻译：

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离散源法分析等离子中非局域性的量子效应

我们考虑了由尺寸小于几十纳米的贵金属纳米粒子组成的等离子体二聚体引起的电磁波散射的数学问题。为了开发数学模型，使用了有效的离散源方法，这使得可以考虑此类系统的所有特殊特征，包括粒子的形状和空间色散的影响（也称为非局部效应）。结果表明，在外部磁场与方位谐波无关的情况下，可以使用在粒子对称轴上的垂直偶极子系统来近似求解问题。基于离散源方法的混合方案，