On the maximal noise for stochastic and QCD traveling waves

TL;DR

This paper investigates the maximum noise level in stochastic traveling wave solutions of nonlinear Langevin equations, with implications for reaction-diffusion processes and quantum chromodynamics, revealing a physical noise limit that can precede phase transitions.

Contribution

It introduces the concept of a maximal noise strength in stochastic traveling waves and analyzes its implications using field-theoretical methods and exact solutions.

Findings

Existence of a maximal noise strength in stochastic traveling waves

The maximal noise limit can occur before the directed percolation transition

An exact solution is available in the quantum chromodynamics context

Abstract

Using the relation of a set of nonlinear Langevin equations with reaction-diffusion processes, we note the existence of a maximal strength of the noise for the stochastic traveling wave solutions of these equations. Its determination is obtained using the field-theoretical analysis of branching-annihilation random walks near the directed percolation transition. We study its consequence for the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. For the related Langevin equation modeling the Quantum Chromodynamic nonlinear evolution of the gluon density with rapidity, the physical maximal-noise limit may appear before the directed percolation transition, due to a shift in the traveling-wave speed. In this regime, an exact solution is known from a coalescence process. Universality and other open problems and applications are discussed in the outlook