Regensburg 2002 – scientific programme

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DY: Dynamik und Statistische Physik

DY 41: Nichtlineare Dynamik I

DY 41.2: Talk

Thursday, March 14, 2002, 10:15–10:30, H3

Logarithmic oscillations in deterministic and stochastic diffusion — •Julia Dräger — I. Institut für theoretische Physik, Universität Hamburg

Oscillations in the logarithm of the time often occur in complex situations like finances, biological systems or quantum survival probabilities. Here we investigate the diffusion which is generated by one dimensional iterated periodic maps. We introduce iterationrules which lead to a logarithmically modulated distribution ψ(t) of waiting times in the corresponding random walk process. We show that in the case where the waiting time distribution is a (modulated) Lévy distribution, is a (modulated) Lévy distribution, ψ(t)∼ t^α with 1<α<2, these oscillations can result in oscillations in the mean squared displacment r²(t) of the corresponding random walk, similiar to the behavior obtained for biased diffusion in percolation systems. In contrast, for waiting time distributions, which decay faster (α>2), the oscillations are washed out in the mean squared displacement.