Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics

M. I. Garcia de Soria 1, P. Maynar 2, 3, G. Schehr 2, A. Barrat 2, E. Trizac 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 051127

We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\em ballistic annihilation} therefore constantly looses particles. The dynamics of perturbations around the free decay regime is investigated from the spectral properties of the linearized Boltzmann operator, that characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of Molecular Dynamics simulations that validate the theoretical predictions.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Laboratoire de Physique Théorique d'Orsay (LPT),
    CNRS : UMR8627 – Université Paris XI - Paris Sud
  • 3. Fisica Teorica, Universidad de Sevilla,
    Universidad de Sevilla