Emergence of pulled fronts in fermionic microscopic particle models

TL;DR

This paper investigates how pulled fronts described by the FKPP equation emerge and behave in a microscopic fermionic particle model, highlighting the role of internal fluctuations controlled by particle number.

Contribution

It explicitly links the deterministic FKPP description with the microscopic fermionic particle model by identifying the fluctuation parameter and analyzing its effects.

Findings

Matching between FKPP and microscopic model when fluctuations are suppressed

Identification of particle number as a key fluctuation control parameter

Demonstration of front emergence in a fermionic lattice model

Abstract

We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A <-> A$ on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. When internal fluctuations are suppressed, we explictly see the matching between the deterministic FKPP description and the microscopic particle model.