Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes

TL;DR

This paper derives the cumulant generating function for a tracer in dense symmetric exclusion processes with quenched initial conditions, revealing how initial states influence tracer diffusion in nonequilibrium dense systems.

Contribution

It provides the first derivation of the cumulant generating function in the dense limit with quenched initial conditions, including biased and step density scenarios.

Findings

Initial conditions significantly affect tracer cumulants.

Derived cumulant generating functions for dense, quenched SEP.

Showed impact of bias on cumulant dependence.

Abstract

The Symmetric Exclusion Process (SEP), where particles hop on a 1D lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions - annealed or quenched - has a quantitative impact on the long-time properties of tracer diffusion. However, so far, all the studies in the quenched case focused on the low-density limit of the SEP. Here, we derive the cumulant generating function of the tracer position in the dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.