Phase coexistence and spatial correlations in reconstituting k-mer models

TL;DR

This paper introduces a matrix product approach to analyze phase coexistence and spatial correlations in reconstituting k-mer models, revealing oscillatory and exponential decay behaviors and a phase coexistence akin to exclusion processes.

Contribution

It provides an analytical matrix product framework for steady states and correlations in reconstituting k-mer models, highlighting phase coexistence and oscillatory correlations.

Findings

Spatial correlations show damped oscillations in certain density regions.

A disorder surface separates oscillatory and exponential decay regimes.

The model exhibits phase coexistence similar to exclusion processes with defects.

Abstract

In reconstituting k-mer models, extended objects which 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.