A phase transition in the dynamics of an exact model for hopping transport

The authors analyse an exact model for hopping transport of a random walker in the presence of randomly distributed deep trapping sites. For an exponential distribution of the depth of traps they find a phase transition in the diffusive behaviour as a function of temperature. They show that above a critical temperature transport is purely diffusive while below it, one finds anomalous diffusion characterised by a diffusion exponent that increases with decreasing temperature. The analysis combines theory with accurate simulation in one and two dimensions. The analytical and numerical results indicate that the upper critical dimension is d_c=2, i.e. for d>or=d_c=2 the mean-field theory can be applied.