Tagged particle motion in a dense liquid: feedback effects from the collective dynamics

The nature of the tagged particle motion in the strongly correlated state of a dense liquid is studied with the self-consistent mode-coupling model. The tagged particle time correlation function psi(s)(q,t) is computed by taking into account the nonlinear feedback effects on its dynamics from the coupling with density fluctuations. We consider the two cases where (a) the short-time dynamics is diffusive resembling colloidal system and (b) the short-time dynamics is Newtonian as in an atomic system. The non-Gaussian parameter alpha(2)(t) is evaluated using the fourth- and second-order spatial moments of the van Hove self-correlation function G(s)(r,t). We observe a two-peaked structure of alpha(2)(t) for both (a) and (b) types of dynamics. We also compare other characteristic aspects of tagged particle dynamics such as the mean square displacement, non-Gaussian nature of G(s)(r,t), and fraction of mobile particles. A qualitative comparison is drawn between the theoretical results with the experimental and computer simulation results on colloids.