Theoretical investigation of anomalous diffusion in a random lattice

The anomalous behavior of the mean square displacement of hopping ions is investigated in a random lattice system by the relaxation mode theory. It is made clear that its short-time behavior, which is linear in time t, is contributed to by the localized nondiffusive modes, and the long-time behavior, also being linear in t, originates from the diffusive mode. In the intermediate time domain, two anomalous regions exist which are universally expressed by 〈ΔR(t)2〉≈C′tk′+Ctk, typically with k′≈0 and k≈0.4: the localized nondiffusive modes result in C′tk′ dominating the shorter-time region while the extended nondiffusive modes govern the longer-time region of Ctk.