Figure 1.

Bethe tree and corresponding ultrametric space, with a branching factor 3. The tiers T₁, T₂, and T₃ are shown. At each branching point, three possible paths on the down-cascading way are considered to be open. Only the terminal points on the bottom actually belong to the ultrametric space; the connecting lines represent (energy) barriers between the sites (see text). The dynamics on an ultrametric space infers that a relaxation of an excited state ● can be achieved by reaching one of the traps *, by a random walk on the branches. The ellipsoids denote the growing radius (ultrametric distance) embracing all sites the excitation can reach within the next step. Note that the sites *₃ and *₄ have the same ultrametric distance D from the original state ●.