Universality of anomalous diffusion in extremely disordered systems Original Research Article

The universal time-dependence of the mean-square displacement for motion in a random energy landscape with equal minima is evaluated analytically and numerically in the percolation path approximation (PPA), which was recently shown by extensive computer simulations in two and three dimensions [Dyre and Schrøder, cond-mat/9601052] to be more accurate than the standard effective medium approximation (EMA). According to the PPA the universal mean-square displacement in dimensionless units as function of time varies as 1/ln2(t−1) for t → 0. This implies a quite different short-time behavior than predicted by the EMA, where the universal mean-square displacement varies as 1/ln(t−1) at short times [Dyre and Jacobsen, Phys. Rev. E 52 (1995) 2429].