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

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.