Trilinear mode effects on transport coefficients

The effects of tri-linear modes on transport coefficients is illustrated by explicit calculations for the self-diffusion constant. In two dimensions the form of the asymptotic time behavior of the velocity autocorrelation function is changed from t^-1 (bilinear modes) to (t log t)^-1 (trilinear modes). Thus, no finite mode calculation in two dimensions can yield the correct asymptotic form. A heuristic self-consistent calculation including all mode orders yields the form t log^{$\text{1}\text{2}$} t]^-1. In three dimensions, the form of the asymptotic time behavior is not changed when higher-order modes are included.