Decoherence and disorder in quantum walks: From ballistic spread to   localization
  We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk and the first Anderson localization in a discrete quantum walk architecture. 
A. Schreiber, K. N. Cassemiro, V. Poto\v{c}ek, A. G\'abris, I. Jex and   Ch. Silberhorn
quant-ph