title: Universal behavior of quantum walks with long-range steps.
abstract: Continuous-time quantum walks with long-range steps R(-gamma) (R being the distance between sites) on a discrete line behave in similar ways for all gamma > or =2 . This is in contrast to classical random walks, which for gamma>3 belong to a different universality class than for gamma < or =3 . We show that the average probabilities to be at the initial site after time t as well as the mean square displacements are of the same functional form for quantum walks with gamma =2, 4, and with nearest neighbor steps. We interpolate this result to arbitrary gamma > or =2 .
authors: Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, Freiburg, Germany. muelken@physik.uni-freiburg.de
authors: Oliver
authors: O
authors: Mülken
authors: Volker
authors: V
authors: Pernice
authors: Alexander
authors: A
authors: Blumen