Quantum diffusion on a cyclic one-dimensional lattice.

The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit N--> infinity is studied.

Random walk with an exponentially varying step.

A random walk with exponentially varying step, modeling damped or amplified diffusion, is studied. Each step is equal to the previous one multiplied by a step factor s (01/s relating different processes.