Inertial effects in the nonlinear transient relaxation of Brownian particles in strong external electric fields

A method of calculation of the nonlinear transient response of an assembly of fixed axis (two-dimensional) rotators due to sudden changes of a strong external dc electric field is presented. The infinite hierarchy of differen tial-recurrence relations for the decay functions describing the relaxation of the system is derived by averaging the underlying inertial Langevin equ ation. The solution for the one-sided Fourier transform of this hierarchy i s obtained in terms of matrix continued fractions. The integral relaxation time and the spectrum of the electric polarization for various kinds of non linear transient responses (step-on, step-off, rapidly rotating field) are calculated for typical values of the model parameters. Both exhibit pronoun ced nonlinear effects due to the strong dc field. Analytical equations for the quantities of interest are presented for particular cases (in the overd amped and low damping limits, etc.). (C) 2001 American Institute of Physics .