# Regensburg 2002 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 41: Nichtlineare Dynamik I

### DY 41.2: Vortrag

### Donnerstag, 14. März 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 *r*^{2}(*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.