On the maximal noise for stochastic and QCD traveling waves

Details On the maximal noise for stochastic and QCD traveling waves On the maximal noise for stochastic and QCD traveling waves

2008-03-18

arxiv.org/abs/0803.2626v1

Nucl.Phys.B805:377-390,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

19 pages, 2 figures

Scientific paper

10.1016/j.nuclphysb.2008.06.010

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

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