Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process

TL;DR

This paper introduces a numerical method to analyze the universal scaling function in a multi-particle discrete-time asymmetric exclusion process, confirming the Derrida-Lebowitz scaling function's applicability even for small system sizes.

Contribution

The paper presents a new numerical approach to directly examine the particle flux in ASEP, enabling verification of the DLSF in discrete-time systems and facilitating studies of complex boundary conditions.

Findings

DLSF accurately describes large system size limit in discrete-time ASEP

Method works effectively for small system sizes (N <= 22)

Enables easier analysis of challenging ASEP dynamics

Abstract

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz's original publication [PRL 80 209 (1998)] this universality has been verified for a variety of continuous time, periodic boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large system size limit (N-->infty) of a single particle discrete time system, even in the case of very small system sizes (N <= 22). This fact allows us to not only verify that the DLSF properly characterizes multiple particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open boundary ASEP.