are systems in which the Langevin model is adequate, namely dilute monodisperse particles suspended in simple Newtonian fluids. The Langevin model provides the solid foundation for particle sizing via quasielastic scattering[@dahneke1983]. For probe diffusion in complex fluids, experiment provides a far more complex picture. Consider a few representative experiments that have determined $P\Delta x, t)$ or $g^{(1s)}(q,t)$ for probe particles in complex fluids.

On relatively long time scales, $P(\Delta x,t)$ is accessible via particle tracking methods. As examples, note experimental studies by Apgar, et al.[@apgar2000a], Tseng and Wirtz[@tseng2001a], and Xu, et al.[@xu2002a] on probe diffusion in glycerol, actin solutions and gels, and gliadin solutions. These authors used video recording and computer image analysis to track simultaneously the motions of large numbers of particles. They report $P(\Delta x, t)$ and $\langle \Delta x(t)^{2} \rangle$ in their systems. Probes in glycerol follow eqs \[eq:gaussianform\] and \[eq:meansquare\]. For probes in various complex fluids, $P(\Delta x, t)$ has decidedly non-Gaussian forms. In these systems, the mean-square displacement does not increase linearly in time. By direct measurement, eq \[eq:gaussianform\] and \[eq:meansquare\] are not uniformly correct for probes in polymer solutions.

Quasielastic scattering spectra of probes in polymer solutions are often markedly non-exponential. For polystyrene latex 