Aggregation-Fragmentation of Clusters in the Framework of gTASEP with Attraction Interaction

Abstract

This article provides summary of some of our results, concerning a model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time discrete-space kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) with open boundaries. The model in essence is the ordinary TASEP with backward ordered sequential update with special kinematic interaction added, i.e., it has a second modified hopping probability $$~{{p}_{m}}$$ for particles in a cluster in addition to the standard hopping probability $$p$$ . We consider separately the two cases of attraction interaction ( $$p$$ < $$~{{p}_{m}}$$ ): (1) the limiting case of irreversible aggregation ( $${{p}_{m}}$$ = 1); and (2) the generic case of attraction, when $$~p$$ < $$~{{p}_{m}}$$ < 1 (then aggregation and fragmentation of clusters is allowed). We put special emphasis on the use of random walk theory in the study of gTASEP. It is applied to study the inter-cluster gaps time evolution, which helps to assess the properties of the nonequilibrium stationary phases of the system and the phase transitions between them. Theoretical conclusions are in agreement with the Monte Carlo simulations.