Self-averaging and ergodicity of subdiffusion in quenched random media

We study the self-averaging properties and ergodicity of the mean square displacement m(t) of particles diffusing in d dimensional quenched random environments which give rise to subdiffusive average motion. These properties are investigated in terms of the sample to sample fluctuations as measured by the variance of m(t). We find that m(t) is not self-averaging for d2 obeys a CTRW, which by itself displays weak ergodicity breaking. This paradox is resolved by the observation that the CTRW as an average model does not reflect the disorder sampling by random motion in a single medium realization.