Particle Ordering in Zero Range Process : Exact spatial correlations of the corresponding exclusion models

TL;DR

This paper develops a method to compute exact spatial correlations in one-dimensional exclusion processes that are equivalent to zero range processes, overcoming the loss of positional ordering in the mapping.

Contribution

The authors introduce a novel method to calculate spatial correlations in exclusion models with ZRP correspondence, enabling analysis of position-dependent correlations.

Findings

Successfully reproduces known correlation results.

Explores previously unexamined correlations in related models.

Provides a general approach applicable to similar exclusion processes.

Abstract

A one dimensional exclusion process is introduced where particles hop to a neighbouring vacant site with a rate that depends on the size of the block they belong to. This model is equivalent to a zero range process (ZRP) and shares the same steady state distribution. However positional ordering is lost in this mapping and spatial correlations which depend on position indices can not be calculated directly from the ZRP equivalence. We devise a method to calculate these correlations and illustrate it by reproducing certain known results. Unexplored correlations in some other model systems are also investigated. This method can be generically used to find exact correlations of one dimensional exclusion processes which has ZRP correspondence.