Anomalous diffusion in quenched trap model on fractal lattices

Tomoshige Miyaguchi, Takuma Akimoto

Published 2014-09-03Version 1

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here, one of such mixed models, the quenched trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble- and time-averaged mean square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergodicity breaking. Moreover, time-averaged MSD exhibits aging and converges to a random variable following the modified Mittag-Leffler distribution. It is also shown that the QTM on a fractal lattice can not be reduced to the continuous-time random walks, if the spectral dimension of the fractal lattice is less than two.