The quantum framework of the time-dependent density functional theory (TDDFT) for analyzing nanostructured devices is reviewed, and alternative methods for incorporating induced electromagnetic fields into the theory are discussed. To capture the retardation effects in larger electronic structures, the TDDFT equations can be formulated by applying the Lorenz gauge-fixing condition to the induced scalar and vector potentials (analogous to macroscopic formulations used in antenna theory). Evaluating the retarded potentials via radiation integrals, however, rapidly becomes the computational bottleneck within the TDDFT time-marching framework if done in a brute-force manner. This article demonstrates that 3D space or 4D space-time fast Fourier transform (FFT) schemes can be adopted to accelerate these computations and reduce the costs of evaluating the potentials below the typical computational bottleneck of TDDFT. Thus, FFT-accelerated Lorenz gauge retarded potentials become an attractive candidate for replacing the conventionally used electrostatic-induced scalar potential within TDDFT.

中文翻译：

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大型量子系统中电磁波现象的建模：公式化和计算成本

审查了时变密度泛函理论（TDDFT）用于分析纳米结构器件的量子框架，并讨论了将感应电磁场纳入该理论的替代方法。为了捕获较大电子结构中的延迟效应，可以通过将Lorenz量规固定条件应用于感应的标量和矢量电势来拟定TDDFT方程（类似于天线理论中使用的宏观公式）。但是，如果以蛮力方式进行操作，则通过辐射积分评估延迟的电势将迅速成为TDDFT时间行进框架内的计算瓶颈。本文演示了可以采用3D空间或4D时空快速傅立叶变换（FFT）方案来加速这些计算，并将评估电势的成本降低到TDDFT的典型计算瓶颈以下。因此，FFT加速的Lorenz规范延迟电位成为替代TDDFT中常规使用的静电感应标量电位的诱人候选物。