Random walks on ultrametric spaces: low temperature patterns

Abstract

The authors present the numerically determined distribution of the number of sites visited by thermally activated walkers on ultrametric spaces, which mimic the energetic disorder found in amorphous materials. At high temperatures the results resemble those found for Sierpinski-type fractals. At low temperatures, the distributions are highly structured, showing discontinuities which increase with the number of steps, in contrast to an intuitive picture that would lead to smoothing. They apply the results to the energy transfer in disordered systems and study the decay due to trapping.