Fracton excitation and Lévy flight dynamics in alkali silicate glasses

We have examined the relaxation behavior of alkali metal ions in lithium metasilicate glasses by means of molecular dynamics simulation. We have observed a change of slope of the mean squared displacement at {~}300fps. In shorter time regions, localized motion of lithium ions within neighboring sites is observed, which is caused by the small fracton dimension (fracton excitation). On the other hand, an accelerated motion of particles due to cooperative jumps is found, which characterizes the diffusion and conduction mechanisms of the alkali metal ions in longer time regions. The dynamics of accelerated motion is discussed in relation to L\'evy flight dynamics.