Anomalous diffusion in a quenched-trap model on fractal lattices

TL;DR

This paper investigates the quenched trap model on fractal lattices, revealing subdiffusive behavior, weak ergodicity breaking, aging phenomena, and the limitations of reducing it to continuous-time random walks based on spectral dimension.

Contribution

It demonstrates that the quenched trap model on fractal lattices exhibits unique subdiffusive and ergodic properties, and cannot be simplified to CTRW models when the spectral dimension is below 2.

Findings

Both ensemble- and time-averaged MSDs show subdiffusion with different exponents.

Time-averaged MSD exhibits aging and converges to a modified Mittag-Leffler distribution.

The model cannot be reduced to CTRW if the spectral dimension is less than 2.

Abstract

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here, one such mixed model, 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 2.