Dynamics of annihilation. II. Fluctuations of global quantities.
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 our attention 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 paper makes use of the spectral analysis reported in the preceding paper [Phys. Rev. E 77, 051127 (2008)].
Maynar
Pablo
P
Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405 Orsay Cedex, France.
García de Soria
María Isabel
MI
Schehr
Grégory
G
Barrat
Alain
A
Trizac
Emmanuel
E