Dynamics of Annihilation II: Fluctuations of Global Quantities

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

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 051128

We develop a theory for fluctuations and correlations in a gas evolving under ballistic annihilation dynamics. Starting from the hierarchy of equations governing the evolution of microscopic densities in phase space, we subsequently restrict to a regime of spatial homogeneity, and obtain explicit predictions for the fluctuations and time correlation of the total number of particles, total linear momentum and total kinetic energy. Cross-correlations between these quantities are worked out as well. These predictions are successfully tested against Molecular Dynamics and Monte-Carlo simulations. This provides strong support for the theoretical approach developed, including the hydrodynamic treatment of the spectrum of the linearized Boltzmann operator. This article is a companion paper to arXiv:0801.2299 and makes use of the spectral analysis reported there.

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