arXiv subjects
Publications and source records attributed to A. Schadschneider.
We present numerical and analytical results for a special kind of one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel automaton. It is shown that the phase boundary separating the active and the recently found chaotic phase exhibits reentrant behavior. Furthermore exact results for the $p_2$=0-line are discussed.
We have found the exact groundstate for a large class of antiferromagnetic spin-1 models with nearest-neighbour interactions on a linear chain. All groundstate properties can be calculated. The groundstate is determined as a matrix product of individual site states and has the properties of the Haldane scenario.
A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental diagram (flow vs.\ density) for parallel dynamics using an improved mean-field approximation which takes into account short-range correlations. For maximum velocity 1 we find that the simplest non-trivial of these approximations gives already the exact result. For higher velocities our results are in excellent agreement with numerical data.
We investigate the excitation spectrum of a model of $N$ colour fermions with correlated hopping which can be solved by a nested Bethe ansatz. The gapless excitations of particle-hole type are calculated as well as the spin-wave like excitations which have a gap. Using general predictions of conformal field theory the long distance behaviour of some groundstate correlation functions are derived from a finite-size analysis of the gapless excitations. From the algebraic decay we show that for increasing particle density the correlation of so-called $N$-multiplets of particles dominates over the density-density correlation. This indicates the presence of bound complexes of these $N$-multiplets. This picture is also supported by the calculation of the effective mass of charge carriers.