Stochastic modelling of ion dynamics in complex systems: dipolar effects

The motion of charge carriers in many solid ionic conductors is determined both by long-range Coulomb interactions and by structural disorder in the host matrix. While the dynamical behaviour at low frequencies is governed by long-range, thermally activated hopping processes, localized motions of the charge carriers with a much weaker temperature dependence can dominate the relaxation spectra at higher frequencies. After a brief summary of the present status of stochastic models in explaining the dynamical behaviour, we focus on the localized degrees of freedom, described as a random lattice of Brownian dipoles. From Brownian dynamics simulations in two dimensions we find an ac response at intermediate frequencies which is of the power-law type, with exponents depending both on temperature and on the degree of randomness. Distinct differences are observed in comparing the collective with the single-dipole response. In particular we discuss our results in relation to the high-frequency 'nearly-constant-loss regime' observed in ion-conducting glasses.