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
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