Anomalous Diffusion in Complex Environments: The Counterintuitive Influence of Obstacles in the Presence of Quenched Disorder

Anomalous diffusion where the mean squared displacement (MSD) does not grow linearly with time t and instead scales as t^α with 0<α<1 has been observed in living cells, glassy materials and many other systems. Counter-intuitively, we show that when the transport is anomalous, presence of obstacles can increase mobility. Simply said, the motion is faster when obstacles are present. We employ analytical and simulation tools to study this surprising effect. Our model consists of a random walker on top of a two dimensional lattice affected by traps or local areas of arrest that cause it to wait after each step. When the waiting times are taken from a heavy-tailed distribution this results in anomalous diffusion. We explore this scenario integrated with a quenched disorder of immobile obstacles. Two popular models of temporal disorder are considered: Continuous Time Random Walk, i.e. representative of annealed disorder, and Quenched Trap Model that represents the quenched disorder case. We show that while in the presence of annealed disorder of waiting times the response to external force decreases with the number of obstacles, it is the quenchness of the waiting times that gives rise to the observed exhibition of motion.