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 reg
ime 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.
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 cons
tantly 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.
