One distinctive feature of the disordered systems is the breadth of their dynamics. It includes picosecond vibrations up to processes, involving the rearrangement of the nanostructure or the diffusive transport, which become observable only over extremely long times, i.e. even weeks or years. Numerical simulations and experiments evidence unexpected strong correlations between the picosecond and the ultra-slow dynamics for a wide class of disordered systems. Here we show that the fast wigglin...