  Non-Gaussian diffusion has been intensively studied in recent years, which
reflects the dynamic heterogeneity in the disordered media. The recent study on
the non-Gaussian diffusion in a static disordered landscape suggests novel
phenomena due to the quenched disorder. In this work, we further investigate
the random walk in this landscape under various effective temperature $\mu$,
which continuously modulates the dynamic heterogeneity. We show in the long
time limit, the trap dynamics on the landscape is equivalent to the quenched
trap model, in which sub-diffusion appears for $\mu<1$. The non-Gaussian
distribution of displacement has been analytically estimated for short $t$, of
which the stretched exponential tail is expected for $\mu\neq1$. Due to the
localization in the ensemble of trajectory segments, an additional peak arises
in $P(x,t)$ around $x=0$ even for $\mu>1$. Evolving in different time scales,
the peak and the tail of $P(x,t)$ are well split for a wide range of $t$. This
theoretical study reveals the connections among the sub-diffusion, non-Gaussian
diffusion, and the dynamic heterogeneity in the static disordered medium. It
also offers an insight on how the cell would benefit from the quasi-static
disordered structures.

Statistical Mechanics;Subcellular Processes