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Stochastic Ballistic Annihilation and Coalescence

R. A. Blythe·M. R. Evans·Y. Kafri
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Abstract

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

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R. A. Blythe, M. R. Evans, Y. Kafri. 2000-10-18. Stochastic Ballistic Annihilation and Coalescence. https://doi.org/10.1103/physrevlett.85.3750

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