Strong anomaly in diffusion generated by iterated maps
We investigate the diffusion generated deterministically by periodic iterated maps that are defined by x(t+1) = x(t)+ax(z)(t)exp[-(b/x(t))(z-1)], z>1. It is shown that the obtained mean squared displacement grows asymptotically as sigma(2)(t) approximately ln (1/(z-1))(t) and that the correspondi...
Saved in:
| Published in | Physical review letters Vol. 84; no. 26 Pt 1; p. 5998 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
26.06.2000
|
| Online Access | Get more information |
Cover
Loading…
| Summary: | We investigate the diffusion generated deterministically by periodic iterated maps that are defined by x(t+1) = x(t)+ax(z)(t)exp[-(b/x(t))(z-1)], z>1. It is shown that the obtained mean squared displacement grows asymptotically as sigma(2)(t) approximately ln (1/(z-1))(t) and that the corresponding propagator decays exponentially with the scaling variable |x|/square root of (sigma(2)(t))]. This strong diffusional anomaly stems from the anomalously broad distribution of waiting times in the corresponding random walk process and leads to a behavior obtained for diffusion in the presence of random local fields. A scaling approach is introduced which connects the explicit form of the maps to the mean squared displacement. |
|---|---|
| ISSN: | 0031-9007 |
| DOI: | 10.1103/physrevlett.84.5998 |