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Memory-induced anomalous dynamics in a minimal random walk model

Harbola, Upendra and Kumar, Niraj and Lindenberg, Katja (2014) Memory-induced anomalous dynamics in a minimal random walk model. In: PHYSICAL REVIEW E, 90 (2).

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Official URL: http://dx.doi.org/ 10.1103/PhysRevE.90.022136

Abstract

A discrete-time dynamics of a non-Markovian random walker is analyzed using a minimal model where memory of the past drives the present dynamics. In recent work N. Kumar et al., Phys. Rev. E 82, 021101 (2010)] we proposed a model that exhibits asymptotic superdiffusion, normal diffusion, and subdiffusion with the sweep of a single parameter. Here we propose an even simpler model, with minimal options for the walker: either move forward or stay at rest. We show that this model can also give rise to diffusive, subdiffusive, and superdiffusive dynamics at long times as a single parameter is varied. We show that in order to have subdiffusive dynamics, the memory of the rest states must be perfectly correlated with the present dynamics. We show explicitly that if this condition is not satisfied in a unidirectional walk, the dynamics is only either diffusive or superdiffusive (but not subdiffusive) at long times.

Item Type: Journal Article
Department/Centre: Division of Chemical Sciences > Inorganic & Physical Chemistry
Depositing User: Id for Latest eprints
Date Deposited: 10 Oct 2014 09:11
Last Modified: 10 Oct 2014 09:11
URI: http://eprints.iisc.ac.in/id/eprint/49973

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