eqs. (\[eq:susceptibilities\]) and (\[eq:abs\]).

[Fig8.eps]{}

Figure \[fig:glass\_lin\_susc\] shows the linear generalized compressibility as a function of temperature for different run times. The compressibility at high temperatures is independent of $T$. In the vicinity of the glass transition $\chi_{l}$ drops. Notice that as the measuring time $t_M$ increases (and hence as the cooling rate decreases), the temperature of the drop decreases and becomes more abrupt. The measuring time can be thought of as the number of snapshots at a single temperature that we use to calculate the compressibility. The linear compressibility is proportional to the width of the distribution of $\rho_{\phi}$, so the drop in $\chi_{l}$ corresponds to the sudden narrowing of the distribution $P(\rho_{\phi})$. If we regard $\rho_{\phi}$ as a generalized center of mass, then the drop in $\chi_{l}$ signals the sudden arrest in the fluctuations of the generalized center of mass. In other words, at the glass transition the motion of the particles is largely frozen and hence, the generalized center of mass does not move around much. This is consistent with recent observations of the colloidal glass transition in which the size of the clusters of “fast” particles drops dramatically at the glass transition [@Weeks00].

Notice that at 