Quantum random walk and transient phenomena

The quantum random walk (QRW) is a new microscopic model for diffusion in a one-dimensional lattice. In order to test its reliability we use the QRW mathematical model to solve the lattice equivalent of the well known perfect-absorbent shutter problem. The QRW is by construction a causal theory; therefore even though our solution lacks for times less than x/v the non-causal behavior, which is characteristic of an exact Moshinsky “diffraction in time” solution, our QRW-derived solution shows for times greater than x/v a damped-oscillatory behavior which resembles the causal Moshinsky solution. Therefore at least for the shutter problem, the oscillatory transient behavior is well approximated by the QRW theory. This gives a confidence test on the model.