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During the last decades, considerable progress has been achieved in the theoretical study of the rotational Brownian motion of particles (or molecules) and relaxation processes in condensed matter, which arises from the application of external stimuli such as electric or magnetic fields [1-71. Among many physical phenomena entering this area of research, one can mention dielectric and Kerr effect relaxation of liquids and liquid crystals as well as magnetic relaxation of single domain (superparamagnetic) particles. All these phenomena can be described in the context of the model of the rotational Brownian motion of a particle both interacting with the thermal environment and subjected to a field of force. The theoretical treatment of these problems is based upon the Langevin equation [8] andfor the Fokker-Planck equation [9] approaches. The Fokker-Planck equation (which is a partial differential equation) describes the time evolution of the orientational distribution function of a particle in configuration (or phase) space. The Langevin equation is a stochastic vector differential equation for angular variables. The Fokker-Planck equation can be directly derived from the Langevin equation by calculating the drift and the diffusion coefficients. However, the statistical averages can be calculated both from the Fokker-Planck and the Langevin equations so that both approaches are completely equivalent.

In this chapter, our analysis will be essentially focused on dielectric and Kerr effect relaxation in strong external electric fields. At the end, we shall present two examples illustrating how to apply the same method to other physical phenomena, such as …