The Gaussian Diffusion Approximation for Complex Fluids is Generally   Invalid
  Simulations are made of a probe particle diffusing through a complex fluid. Probe particle motions are described by the Mori-Zwanzig equation and Mori's orthogonal hierarchy of random forces scheme, subject to the approximation that the fluid creates a rapidly-fluctuating random force corresponding to solvent motions and a slowly fluctuating random force corresponding to solute (e.~g., matrix polymer) motions. The Gaussian diffusion approximation is seriously incorrect in this physically-plausible model system. $P(x,t)$ has exponential wings. $g^{(1s)}(q,t)$ can differ from $\exp(-q^{2} \langle x^{2}\rangle/2)$ by up to orders of magnitude. Experimental interpretations that rely on the Gaussian approximation, such as the Stejskal-Tanner equation for pulsed-field-gradient NMR or particle tracking, can not be assumed to be reliable in complex fluids. 
George D. J. Phillies
cond-mat.soft