On the maximal noise for stochastic and QCD traveling waves
arXiv:0803.2626 · doi:10.1016/j.nuclphysb.2008.06.010
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
19 pages, 2 figures
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