Stochastic ballistic annihilation and coalescence

We study a class of stochastic ballistic annihilation and coalescence model s with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the as ymptotic density decay. By universal we mean that all models in the class a re described by a single phase diagram spanned by two reduced parameters. T he phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct co nsequence of the stochasticity. The solution is obtained through a matrix p roduct approach and builds on properties of a q-deformed harmonic oscillato r algebra.