We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact, analytical solution of the model yields the transient behavior...

The quantal diffusion of a particle with an initial velocity coupled to a non-Ohmic environment passing over a potential top is considered. It is shown that sub- and super-diffusions hinder the directional motion of the particle in two different ways. The former makes the particle have a strong...

Dimension-invariance approach, a dimension-stretching analogue of scale-stretching invariance, is developed for classical and quantum multifractal systems. It is shown, by comparison with laboratory and numerical experiments of different authors, that dimensions-invariance takes place in quantum...