Structural dynamics of a model of amorphous silicon

We perform extensive simulations and systematic statistical analyses of the structural dynamics of amorphous silicon. The simulations follow the dynamics introduced by Wooten, Winer and Weaire: the energy is obtained with the Keating potential, and the dynamics consists of bond transpositions proposed at random locations and accepted with the Metropolis acceptance ratio. The structural quantities we track are the variations in time of the lateral lengths ($L_x$,$L_y$,$L_z$) of the cuboid simulation cell. We transform these quantities into the volume $V$ and two aspect ratios $B_1$ and $B_2$. Our analysis reveals that at short times, the mean squared displacement (MSD) for all of them exhibits normal diffusion. At longer times, they cross over to anomalous diffusion, with a temperature-dependent anomalous exponent $\alpha<1$. We analyze our findings in the light of two standard models in statistical physics that feature anomalous dynamics, $viz.$, continuous time random walker (CTRW) and fractional Brownian motion (fBm). We obtain the distribution of waiting times, and find that the data are consistent with a stretched-exponential decay. We also show that the three quantities, $V$, $B_1$ and $B_2$ exhibit negative velocity autocorrelation functions. These observations together suggest that the dynamics of the material belong to the fBm class.