Regensburg 2000 – scientific programme
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DY: Dynamik und Statistische Physik
DY 45: Niedrigdimensionales Chaos
DY 45.4: Talk
Thursday, March 30, 2000, 15:30–15:45, H3
Strong Anomaly in Subdiffusion Generated by an Iterated Map — •Julia Dräger1 and Joseph Klafter2 — 1I. Inst. f. theoret. Physik, Jungiusstr. 9, 20355 Hamburg — 2School of Chemistry, Tel-Aviv University, Tel-Aviv, Israel
We investigate the diffusion generated deterministically by periodic iterated maps that are defined by xt +1 =xt +axt zexp[−(1/xt )z−1] for 0≤ xt <0.5 with z>1. It is shown that the obtained mean squared displacement grows asymptotically like ⟨x 2(t) ⟩∼ ln1/(z−1) (t), a property which stems from an anomalously slow decay of the waiting time distribution in the corresponding random walk process. The latter leads to a propagator which is exponential in the scaling variable x /√ ⟨x2(t) ⟩. A scaling approach is introduced which connects on more general grounds the explicit form of the map to the corresponding mean squared displacement.