title: Correlated continuous-time random walks in external force fields.
abstract: We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T_{i} is equal to the previous waiting time T_{i-1} plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.
authors.affiliation: Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland. marcin.magdziarz@pwr.wroc.pl
authors.forename: Marcin
authors.initials: M
authors.lastname: Magdziarz
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler
authors.forename: Wladyslaw
authors.initials: W
authors.lastname: Szczotka
authors.forename: Piotr
authors.initials: P
authors.lastname: Zebrowski