Universal behavior of quantum walks with long-range steps.
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 .
Mülken
Oliver
O
Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, Freiburg, Germany. muelken@physik.uni-freiburg.de
Pernice
Volker
V
Blumen
Alexander
A