7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 t  [ns] 10 -4 10 -3 10 -2 10 -1 10 0 10 1 r 2 (t w ,t w +t)  [ Å 2 ] t$_{w}$=0  ns t$_{w}$=24.0  ns O-atoms 10 -4 10 -3 10 -2 10 -1 10 0 10 1 t$_{w}$  [ns] 10 -4 10 -3 10 -2 10 -1 10 0 10 1 t r msd (t w ) [ns] T$_{f}$= 2500 K 2750 K 3000 K 3250 K 2500 K 2750 K 3000 K 3250 K  O-atoms T$_{i}$=3760 K T$_{i}$=5000 K FIG. 11: (Color online) t msd r for O-atoms. Symbols for the dif- ferent ( T i , T f ) combinations are the same as in Fig. 7. Error bars are indicated exemplary for ( 3760 K, 2500 K), ( 5000 K, 2500 K) and ( 5000 K, 3000 K). FIG. 10: (Color online) Mean square displacement Δ r $^{2}$( t w , t w + t ) as defined in Eq. (7) for the temperature quench from 5000 K to 2500 K and for O-atoms. Waiting times and corresponding line styles are the same as in Fig. 4. C. Mean Square Displacement In the previous section, we have focused on the analysis of C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) and identified different time-windows. In this section, we consider the mean square displacement Figure 10 shows Δ r $^{2}$( t$_{w}$, t$_{w}$ + t ) for the temperature quench from 5000 K to 2500 K and for O-atoms. As in Fig. 4, for times t ≲ 5 · 10 − $^{5}$ns and zero waiting time, the mean square displacement Δ r $^{2}$( t$_{w}$ = 0 , t ) is well ap- proximated by Δ r 2 of the high temperature T$_{i}$ = 5000 K from which the system has been quenched (see dashed line in Fig. 10) and thus independent of T$_{f}$ . For times t ≈ 10 − $^{3}$ns, Δ r $^{2}$( t$_{w}$, t$_{w}$ + t ) is oscillatory due to the small system size [31], while for times t ≳ 10 − $^{3}$ns and waiting times t$_{w}$ ≥ 0 . 33 ns, we find that Δ r 2 forms a plateau which is independent of t$_{w}$ . As for C$_{q}$ , we find that the plateau is the more horizontal the smaller T$_{f}$ and the plateau height depends on the particle type but is inde- pendent of T$_{i}$ . For waiting times t$_{w}$ ≥ 0 . 33 ns and times t ≳ 0 . 1 ns, the mean square displacement leaves the plateau and in- creases further. To characterize the dependence of this α -relaxation we define the time t msd r as the time t = t msd r for which Δ r $^{2}$( t$_{w}$, t$_{w}$ + t msd r ) = 1 . 35 ˚ A 2 (see Fig. 11). We can identify again the three time windows (I) of waiting times t$_{w}$ ≲ 0 . 3 ns with a dependence on T$_{i}$ , T$_{f}$ and particle type, (II) the aging regime of intermediate waiting times where t msd r follows roughly a power law, and (III) for very long waiting times when equilibrium is reached. The transition from (II) to (III) occurs at approximately the same times t$_{23}$ as for C$_{q}$ , i.e. t$_{23}$ ≈ 0 . 3 ns for T$_{f}$ = 3250K, t$_{23}$ ≈ 1 ns for T$_{f}$ = 3000 K, t$_{23}$ ≈ 3 ns for T$_{f}$ = 2750 K and t$_{23}$ ≈ 10 ns for T$_{f}$ = 2500 K. Figure 12 shows the equivalent of Fig. 8 to test time superposition. We find for Δ r $^{2}$( t/t msd r ) that time super- position is valid for waiting times 0 . 34 ns ≤ t$_{w}$ ≲ 8 . 83 ns, i.e. for the time window (II) but not for the time window (III). FIG. 12: (Color online) Δ r $^{2}$( t/t msd r ) for the temperature quench from 5000 K to 2500 K and for O-atoms. Δ r $^{2}$( t$_{w}$, t$_{w}$ + t ) = 1 N N ∑ i =1 〈 ( r$_{i}$ ( t$_{w}$ + t ) − r$_{i}$ ( t$_{w}$ )) 2 〉 . (7) 10 -2 10 -1 10 0 10 1 t /t$_{r}$ msd 10 0 10 1 r 2 (t w ,t w +t)  [ Å 2 ] t$_{w}$=0.49  ns 1.17  ns 1.96  ns 8.83  ns 16.67  ns 23.98  ns t$_{w}$=0.49  ns t$_{w}$=24.0  ns O-atoms