Budó’s generalization [A. Budó, J. Chem. Phys. 17, 686 (1949)] of the Debye rotational diffusion model of dielectric relaxation of polar molecules to an assembly with internal interacting polar groups is extended to inertial anomalous diffusion. Thus, the theory can be applied both in the GHz and the THz regions, accounting for anomalous behavior as well as the necessary return to optical transparency at very high frequencies. The linking of both dispersion regions in a single model including anomalous effects is accomplished via a fractional Fokker-Planck equation in phase space based on the continuous time random walk ansatz. The latter is written via the Langevin equations for the stochastic dynamics of pairs of interacting heavy polar groups embedded in the frame of reference of a particular molecule or molecular dimer rotating about a space-fixed axis. The fractional Fokker-Planck equation is then converted to a three-term matrix differential recurrence equation for the statistical moments. This is solved in the frequency domain for the linear dielectric response using matrix continued fractions. Thus, one has the complex susceptibility $\chi \left(\omega \right)$ for extensive ranges of damping, group dipole moment ratio, and friction. The susceptibility, as inferred from the small oscillation limit, inherently comprises a low frequency (GHz) band with width depending on the anomalous parameter and a far-infrared (THz) or Poley peak of resonant character with a comblike structure of harmonic peaks. This behavior is due to the double transcendental nature of the after-effect function.

中文翻译：

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具有旋转极性基团的分子的异常扩散：惯性和偶极耦合在微波和远红外吸收中共同起的作用

布多的概括[A. Budó，化学杂志。物理 17极性分子的介电弛豫的德拜旋转扩散模型与内部相互作用的极性基团的组件的，686（1949）]扩展到惯性异常扩散。因此，该理论可以在GHz和THz区域中应用，这说明了异常行为以及在非常高的频率下必须恢复到光学透明的情况。两分散体的区域在所述连接单基于连续时间随机游走ansatz的相空间中的分数Fokker-Planck方程可完成包含异常效应的模型。后者是通过Langevin方程编写的，该函数用于嵌入在围绕固定空间轴旋转的特定分子或分子二聚体的参照系中的成对相互作用的重极性基团对的随机动力学。然后将分数Fokker-Planck方程转换为统计矩的三项矩阵微分递推方程。使用矩阵连续分数在线性电介质响应的频域中解决了这一问题。因此，人们具有复杂的敏感性$\chi （\omega ）$适用于广泛的阻尼，群偶极矩比和摩擦力。从小的振荡极限可以推断出，磁化率固有地包括一个低频（GHz）频带，其宽度取决于异常参数，以及一个谐振特性的远红外（THz）或Poley峰，具有谐波峰的梳状结构。此行为归因于后效应功能的双重超越特性。