Anomalous diffusion through coupling to a fractal environment: Microscopicderivation of the "whip-back" effect

Two models for quantum Brownian motion the Oscillator Bath (OB) model and t he Random Band-Matrix (RBM) model are compared and a relation between the s pectral density function I (omega) and the variance <(V-ab(2))over bar> 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-co rrelation function (VACF) is entirely determined by the band form factor. T his allows for a microscopic derivation of the "whip-back" effect.