An exactly soluble noisy traveling wave equation appearing in the problem of directed polymers in a random medium

Details An exactly soluble noisy traveling wave equation appearing in the problem of directed polymers in a random medium An exactly soluble noisy traveling wave equation appearing in the problem of directed polymers in a random medium

2004-09-10

arxiv.org/abs/cond-mat/0409261v1

Phys. Rev. E 70, 016106 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages

Scientific paper

10.1103/PhysRevE.70.016106

We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of $N$ evolving particles which can be described by a noisy traveling wave equation with a noise of order $N^{-1/2}$. Our model can be viewed as the infinite range limit of a directed polymer in random medium with $N$ sites in the transverse direction. Despite some peculiarities of the traveling wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle.

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