Phase separation transition of reconstituting k-mers in one dimension

TL;DR

This paper models one-dimensional driven diffusive systems with reconstituting k-mers, revealing phase transitions including fluid, macroscopic k-mers, and void formations, with exact phase boundaries derived.

Contribution

It introduces a new driven diffusive model with size-dependent drive and reconstitution, mapping it to a misanthrope process, and analytically determines phase boundaries.

Findings

Identification of fluid, macroscopic k-mer, and void phases.

Exact phase boundaries for different phases.

Reconstitution and drift interplay causes phase transitions.

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.