We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one dimensional ring, where the walkers hop to their nearest neighbor with a bias ǫ. For ǫ = 0, three universality classes: directed percolation (DP), parity conserving (PC) and pair contact process with diffusion (PCPD) are typically observed in such systems. We find that the introduction of ǫ does not change the DP universality class but alters the other two universality classes. For non-zero ǫ, the PCPD class crosses over to DP and the PC class changes to a new universality class. * bijoydaga@imsc.res.in † ray@imsc.res.in
We introduce a driven diffusive model involving poly-dispersed hard k-mers on a one dimensional periodic ring and investigate the possibility of phase separation transition in such systems. The dynamics consists of a size dependent directional drive and reconstitution of k-mers. The reconstitution dynamics constrained to occur among consecutive immobile k-mers allows them to change their size while keeping the total number of k-mers and the volume occupied by them conserved. We show by mapping the model to a two species misanthrope process that its steady state has a factorized form. Along with a fluid phase, the interplay of drift and reconstitution can generate a macroscopic k-mer, or a slow moving k-mer with a macroscopic void in front of it, or both. We demonstrate this phenomenon for some specific choice of drift and reconstitution rates and provide exact phase boundaries which separate the four phases.
In reconstituting k-mer models, extended objects that occupy several sites on a one-dimensional lattice undergo directed or undirected diffusion, and reconstitute-when in contact-by transferring a single monomer unit from one k-mer to the other; the rates depend on the size of participating k-mers. This polydispersed system has two conserved quantities, the number of k-mers and the packing fraction. We provide a matrix product method to write the steady state of this model and to calculate the spatial correlation functions analytically. We show that for a constant reconstitution rate, the spatial correlation exhibits damped oscillations in some density regions separated, from other regions with exponential decay, by a disorder surface. In a specific limit, this constant-rate reconstitution model is equivalent to a single dimer model and exhibits a phase coexistence similar to the one observed earlier in totally asymmetric simple exclusion process on a ring with a defect.
We study an interacting box-particle system on a one-dimensional periodic ring involving two species of particles A and B. In this model, from a randomly chosen site, a particle of species A can hop to its right neighbor with a rate that depends on the number of particles of the species B at that site. On the other hand, particles of species B can be transferred between two neighboring sites with rates that depends on the number of particles of species B at the two adjacent sites−this process however can occur only when the two sites are devoid of particles of the species A. We study condensation transition for a specific choice of rates and find that the system shows a reentrant phase transition of species A − the species A passes successively through fluid-condensate-fluid phases as the coupling parameter between the dynamics of the two species is varied. On the other hand, the transition of species B is from condensate to fluid phase and hence does not show reentrant feature.
We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state-the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between the above phases are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.