Generalized Quantum Walk in Momentum Space
arXiv:quant-ph/0408183 · doi:10.1016/j.physa.2005.01.026
Abstract
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known quantum kicked rotor, this model can be mapped into a localized one-dimensional Anderson model. For exceptional (rational) values of its scale parameter, the system exhibits resonant behavior and reduce to the usual discrete time quantum walk on the line.
11 pages, 5 figures