Mass fluctuations in Random Average Transfer Process in open set-up

TL;DR

This paper introduces a new mass transport model on a one-dimensional lattice with reservoirs, analyzing non-equilibrium steady states and multi-site cumulants using an innovative operator method supported by simulations.

Contribution

It develops a novel operator approach to compute multi-site cumulants in a mass transport model, revealing the dependence on lower order cumulants unlike Wick's theorem.

Findings

Multi-site cumulants expand in powers of 1/N with scaling forms.

Higher order cumulants depend on all lower order cumulants.

Monte-Carlo simulations support the theoretical results.

Abstract

We define a new mass transport model on a one-dimensional lattice of size $N$ with continuous masses at each site. The lattice is connected to mass reservoirs of different `chemical potentials' at the two ends. The mass transfer dynamics in the bulk is equivalent to the dynamics of the gaps between particles in the Random Average Process. In the non-equilibrium steady state, we find that the multi-site arbitrary order cumulants of the masses can be expressed as an expansion in powers of $1/N$ where at each order the cumulants have a scaling form. We introduce a novel operator approach which allows us to compute these scaling functions at different orders of $1/N$. Moreover, this approach reveals that, to express the scaling functions for higher order cumulants completely one requires all lower order multi-site cumulants. This is in contrast to the Wick's theorem in which all higher order cumulants are expressed solely in terms of two-site cumulants. We support our results with evidence from Monte-Carlo simulations.