Coffey William T, Kalmykov Yuri P, Titov Sergey V
Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland.
J Chem Phys. 2007 Feb 28;126(8):084502. doi: 10.1063/1.2463694.
It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.
本文展示了如何通过使用分数动力学方程，将极性分子的旋转扩散模型（从微观角度可描述为单位球面上离散时间随机游走的扩散极限）扩展到反常非线性介电弛豫和动态克尔效应。该分数动力学方程（通过将传统旋转扩散的非惯性动力学方程推广到分数动力学以包含反常弛豫而得到）使用矩阵连分数求解，得出了由任意强度的外部叠加直流电场(E_0)和交流电场(E_1(t)=E_1\cos\omega t)作用的刚性偶极粒子集合的复非线性介电常数和克尔函数。在弱场极限下，还推导了非线性响应函数的解析方程。
