Randomwalk model for kink-antikink annihilation in a fluctuating environment

In this report, the kink-antikink interaction, in one spatial dimension, is revised in the framework of a paradigmatic model for bistability (real Ginzburg- Landau equation). In particular, it is pointed out that, when it is taking into account the fluctuations, drastically changes the main features of the interaction. To wit, since the long distance interaction is exponentially weak, the kink-antikink movement is ruled by the fluctuations. A simple random walk model, that incorporates the pair self-annihilation, is proposed. We discussed the implications that, consider the fluctuations, has in the coarsening dynamics. That is, the coarsening law, for the growing of the domains in each stable state, changes from being logarithmic to becoming in the power law √ t.