Abstract. In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type of state is also obtained for an ASEP on a ring in which particles can move one or two sites. The dynamics leads to the formation of an excess hole that plays the role of a defect. We expect the process to play a similar role for parallel dynamics as the well-known ASEP with a single defect-particle (that is obtained in the continuoustime limit) especially for the study of shocks. The process exhibits a first-order phase transition between two phases with different defect velocities. These are calculated exactly from the process-generating function.

A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent ξ −1 . We determine the exact value of ξ −1 of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all higher even-order generalized Lyapunov exponents can be calculated, as exemplified for fourth order. An approximation for the localization length (inverse standard Lyapunov exponent) is presented, by assuming a log-normal limiting distribution for the dimensionless conductance T . This approximation works well in the limit of weak disorder, with the exception of the band edges and the band center.

A bottleneck situation in one-lane traffic flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal realization of this mechanism to which we refer to as density-feedback control (DFC): If the actual density in the bottleneck is above a certain threshold, the reservoir density of possibly entering cars is reduced to a different constant value. By numerical solution of the discretized viscid Burgers equation a rich stationary phase diagram is found. In order to maximize the flow, which is the goal of typical traffic-management strategies, we find the optimal choice of the threshold. Analytical results are verified by computer simulations of the microscopic totally asymmetric exclusion process with DFC.

Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. In this work a model of pedestrian motion is presented that is able to reproduce oscillations with different characteristics. The Wald-Wolfowitz test and Gillis' correlated random walk are shown to include observables that can be used to characterize different kinds of oscillations.

A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular automata for traffic flow with non-local jumps for the kinetic constraint to drive as fast as possible. The exactly solvable model shows a discontinuous phase transition between two regions with different cargo velocities.