Two-level model for the nonexponential Williams-Watts dielectric relaxation.

A model of low-frequency dielectric relaxation in condensed matter is proposed. A dipolar system with a very simple Hamiltonian which will allow us to obtain its response function from microscopic properties has been taken. This function has been calculated by means of two methods: the Kubo formalism and one using a time-dependent transition rate which, introduced in an appropriate master equation, allows us to obtain the above-mentioned function. We show that under certain conditions both methods lead to the same result, which depends on the choice of several parameters. The Williams-Watts function, which is one of the most widely used for describing several kinds of relaxations for many diverse systems, is shown to be a convenient one.