Quenched trap model on the extreme landscape: The rise of subdiffusion and non-Gaussian diffusion

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 paper, we further investigate the random walk on this landscape under various effective temperatures mu, which continuously modulate 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 subdiffusion 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 not equal 1. 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 timescales, the peak and the tail of P(x, t) are well split for a wide range of t. This theoretical paper reveals the connections among the subdiffusion, 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 quasistatic disordered structures.