Phase separation transition of reconstitutingk-mers in one dimension

Abstract

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.

Reentrant condensation transition in a two species driven diffusive system

“…Therefore the phase separation transition in the corresponding lattice map [23] of the model studied here is also expected to show a reentrant behavior. Finally, we think that it would be interesting to find out if reentrant phase behavior could also be observed in a more general class of DDS, namely the finite-range processes which provide cluster factorised steady states [34].…”

“…However, in this case there is an additional restriction that the boxes exchanging particles of species B are devoid of particles of the species A. This condition is crucial for explicit factorization of the steady state [23]. Depending on whether a B-type particle is transferred from site i to i + 1 or vice-versa, we define w(n i , n i+1 ) or w(n i+1 , n i ) to be the corresponding rates for the dynamics of species B.…”

“…The dynamics of the species B is similar to that of a misanthrope process [28,29] and hence the rate of diffusion depends on the number of particles in both departure and the arrival site. It is necessary to mention here that in the model of reconstituting k-mers, particles of species A corresponds to 0-particles and that of species B corresponds to k-particles [23].…”

“…However, when the density of species A is not equal to zero (z > 0 case), (ρ For a given value of k, the nature of condensation is found to be different for the regimes v < 1 and v > 1 [23]. For ρ A > 0, the background critical densities can be found out from the grand canonical measure by using the Großkinsky theorem [31].…”

A simple non-equilibrium, statistical-physics toy model of thin-film growth

“…These models share a common feature: the steady-state probability of a microstate can be expressed analytically as a function of transition rates which define the dynamics of the model. Examples of such systems are the zero-range process (ZRP) [2,3,4], closely related to its equilibrium counterpart: balls-in-boxes model (B-in-B) [5], the asymmetric simple exclusion process (ASEP) [6] and its totally asymmetric version (TASEP) [7], asymmetric inclusion process (ASIP) [8,9,10] and many variations on these two models [11,12,13,14,15]. In all these models, particles jump between sites of a one-or higher-dimensional lattice and the dynamics is defined by specifying the hopping rates of the particles.…”