$T=0.1$ and becomes stronger as the temperature is lowered. This separation of the two time scales is due to the weaker temperature dependence of the diffusion coefficient. That is, diffusion is relatively enhanced at lower temperatures. This is quite analogous to the violation of the SE relation ($D=T/a \eta$, where $a$ is a molecular length and $\eta$ is the viscosity of the liquid) observed in experiments on supercooled liquids [@fujara]. Here, we mention that there exists a correlation between the increase of non-exponentiality (as the temperature is lowered) and the increase of the product $4 D\tau$ at low temperatures [@ediger].

If we suppose that there exists a single dominant relaxation mode in the system (and hence one relaxation time scale $\tau$), then we would obtain a simple exponential behavior for the relaxation function $C(t) \sim e^{-t/\tau}$. On the other hand, if the system consists of many regions with different relaxation times, then the relaxation function would be roughly some superposition of exponentials with a broad distribution of relaxation times, which would be in general not expressible in a simple exponential form, but in stretched exponetial form or other more complicated forms.

The fact that there exists a breakdown of proportionality 