2000/05/31 by P. L. Krapivsky, Paul L. Kaprivsky, Clément Sire · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.86.2494
published as Phys. Rev. Lett. 86, 2494 (2001) · 4 RevTeX pages and 1 Eps figure; submitted to Phys. Rev. Lett
arxiv created 2000/05/31 · openalex publication_date 2001/03/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of the Boltzmann equation. The particle density and the rms velocity decay as c\ensuremath∼t^\ensuremath-\ensuremathα and v\ensuremath∼t^\ensuremath-\ensuremathβ, with the exponents depending on the initial velocity distribution and the spatial dimension d. For instance, in one dimension for the uniform initial velocity distribution \ensuremathβ\phantom\rule0ex0ex=\phantom\rule0ex0ex0.230472… . In the opposite extreme d\ensuremath→\ensuremath∞, the dynamics is universal and \ensuremathβ\ensuremath→(1\ensuremath-2^\ensuremath-1/2)d^\ensuremath-1. We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.