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 I(w) and the variance (Vab)^2 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.
@article{arxiv.cond-mat/0004041,
title = {Anomalous diffusion through coupling to a fractal environment: Microscopic derivation of the "whip-back" effect},
author = {E. Lutz},
journal= {arXiv preprint arXiv:cond-mat/0004041},
year = {2009}
}