6 research outputs found
Nonstationary generalized TASEP in KPZ and jamming regimes
We study the model of the totally asymmetric exclusion process with
generalized update, which compared to the usual totally asymmetric exclusion
process, has an additional parameter enhancing clustering of particles. We
derive the exact multiparticle distributions of distances travelled by
particles on the infinite lattice for two types of initial conditions: step and
alternating once. Two different scaling limits of the exact formulas are
studied. Under the first scaling associated to Kardar-Parisi-Zhang (KPZ)
universality class we prove convergence to the universal Airy and Airy
processes. Under the second scaling we prove convergence to two new random
processes, which describe the transition between the KPZ regime and the
deterministic aggregation regime, in which the particles stick together into a
single giant cluster moving as one particle. It is shown that the transitional
distributions have the Airy processes and fully correlated Gaussian
fluctuations as limiting cases. We also give the heuristic arguments explaining
how the non-universal scaling constants appearing from the asymptotic analysis
in the KPZ regime are related to the properties of translationally invariant
stationary states in the infinite system and how the parameters of the model
should scale in the transitional regime.Comment: 72 pages, 5 figure
The totally asymmetric exclusion process with generalized update
We consider the totally asymmetric exclusion process in discrete time with
generalized updating rules. We introduce a control parameter into the
interaction between particles. Two particular values of the parameter
correspond to known parallel and sequential updates. In the whole range of its
values the interaction varies from repulsive to attractive. In the latter case
the particle flow demonstrates an apparent jamming tendency not typical for the
known updates. We solve the master equation for particles on the infinite
lattice by the Bethe ansatz. The non-stationary solution for arbitrary initial
conditions is obtained in a closed determinant form.Comment: 11 pages, 3 figure