| Issue |
Europhys. Lett.
Volume 54, Number 3, May 2001
|
|
|---|---|---|
| Page(s) | 293 - 299 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2001-00240-x | |
| Published online | 01 December 2003 | |
Anomalous diffusion through coupling to a fractal environment: Microscopic derivation of the "whip-back"effect
Max-Planck-Institut für Kernphysik -
Postfach 103980, 69029 Heidelberg, Germany
Received:
31
August
2000
Accepted:
21
February
2001
Two models for quantum Brownian motion -the Oscillator Bath (OB)
model and the Random Band-Matrix (RBM) model-are compared and a
relation between the spectral density function 
and the
variance 
is established. The extension to a
fractal environment is then considered and the microscopic origin of
anomalous diffusion is discussed. In particular, it is shown that the
asymptotic behavior of the normalized velocity auto-correlation
function (VACF) is entirely determined by the band form factor. This
allows for a microscopic derivation of the "whip-back"effect.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.Df – Fractals
© EDP Sciences, 2001
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