title: Space-time velocity correlation function for random walks.
abstract: Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. Here we adopt this concept for single-particle random walks and demonstrate that the corresponding space-time velocity autocorrelation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nanoscales.
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
authors.forename: V
authors.initials: V
authors.lastname: Zaburdaev
authors.forename: S
authors.initials: S
authors.lastname: Denisov
authors.forename: P
authors.initials: P
authors.lastname: Hänggi