Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland.
Laboratoire de Mathématiques et de Physique (LAMPS, EA4217), Université de Perpignan Via Domitia, F-66860, Perpignan, France.
Phys Rev E. 2016 Apr;93:042208. doi: 10.1103/PhysRevE.93.042208. Epub 2016 Apr 14.
External dc bias-field effects on the nonlinear dielectric relaxation and dynamic Kerr effect of a system of permanent dipoles in a uniaxial mean-field potential are studied via the rotational Brownian motion model postulated in terms of the infinite hierarchy of differential-recurrence equations for the statistical moments f_{n}(t)=〈P_{n}〉(t) (the expectation value of the Legendre polynomials P_{n}). By solving these equations, the nonlinear dielectric and Kerr-effect ac stationary responses are evaluated for arbitrary dc field strength via perturbation theory in the ac field. Simple analytic equations based on the large separation of the time scales of the fast intrawell and slow overbarrier (interwell) relaxation processes are also derived.
通过基于无穷微分递归方程的统计矩 f_{n}(t)=〈P_{n}〉(t)（Legendre 多项式 P_{n}的期望）的旋转布朗运动模型，研究了外直流偏置场对单轴平均场势中永久偶极子系统的非线性介电弛豫和动态克尔效应的影响。通过求解这些方程，我们通过交流场中的微扰理论评估了任意直流场强下的非线性介电和克尔效应交流稳态响应。还基于快速腔内和慢超势（腔内）弛豫过程的时间尺度大分离的简单解析方程也被推导出来。
