2000/05/31 by Richard A. Blythe, R. A. Blythe, M. R. Evans +2 · 1 citation
Mathematics · Physics and Astronomy · #Annihilation #Binary number #Coalescence (physics) #Creation and annihilation operators #Harmonic oscillator #Mathematics #Phase (matter) #Phase diagram #Physics #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.85.3750
published as Phys. Rev. Lett. (2000) v 85 no 18 pp 3750-3753 · 4 pages RevTeX, 3 figures; revised version with some corrections, additional discussion and in RevTeX format
arxiv created 2000/10/18 · openalex publication_date 2000/10/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.