  Diffusion on a quenched heterogeneous environment in the presence of bias is
considered analytically. The first-passage-time statistics can be applied to
obtain the drift and the diffusion coefficient in periodic quenched
environments. We show several transition points at which sample-to-sample
fluctuations of the drift or the diffusion coefficient remain large even when
the system size becomes large, i.e., non-self-averaging. Moreover, we find that
the disorder average of the diffusion coefficient diverges or becomes zero when
the corresponding annealed model generates superdiffusion or subdiffusion,
respectively. This result implies that anomalous diffusion in an annealed model
is traced by anomaly of the diffusion coefficients in the corresponding
quenched model.
