A fractional Fokker–Planck equation based on the continuous time random walk Ansatz is written via the Langevin equations for the dynamics of a dipole interacting with its surroundings, as represented by a cage of dipolar molecules. This equation is solved in the frequency domain using matrix continued fractions, thus yielding the linear dielectric response for extensive ranges of damping, dipole moment ratio, and cage–dipole inertia ratio, and hence the complex susceptibility. The latter comprises a low frequency band with width depending on the anomalous parameter and a far infrared (THz) band with a comb-like structure of peaks. Several physical consequences of the model relevant to anomalous diffusion in the presence of interactions are discussed. The entire calculation may be regarded as an extension of the cage model interpretation of the dynamics of polar molecules to anomalous diffusion, taking into account inertial effects.

中文翻译：

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偶极子与其周围环境相互作用的异常扩散

基于连续时间随机游动Ansatz的分数Fokker-Planck方程通过Langevin方程写出偶极子与其周围环境相互作用的动力学，以偶极子分子的笼子为代表。使用矩阵连续分数在频域中求解该方程，从而在宽范围的阻尼，偶极矩比和保持架-偶极惯性比以及复杂磁化率范围内得出线性介电响应。后者包括宽度取决于异常参数的低频带和具有峰状梳状结构的远红外（THz）频带。讨论了与存在相互作用的异常扩散有关的模型的几种物理结果。整个计算可以看作是笼型模型解释的扩展，该模型解释了极性分子对异常扩散的动力学，