title: Memory-induced anomalous dynamics in a minimal random walk model.
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.
authors.affiliation: Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore, Karnataka 560012, India.
authors.forename: Upendra
authors.initials: U
authors.lastname: Harbola
authors.affiliation: Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.
authors.forename: Niraj
authors.initials: N
authors.lastname: Kumar
authors.affiliation: Department of Chemistry and Biochemistry, and BioCircuits Institute, University of California San Diego, La Jolla, California 92093-0340, USA.
authors.forename: Katja
authors.initials: K
authors.lastname: Lindenberg
mesh_terms: D004058:Diffusion; D008962:Models, Theoretical; D011336:Probability