Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics

TL;DR

This paper investigates the non-equilibrium dynamics of ballistic annihilation systems by analyzing the linearized Boltzmann equation, deriving hydrodynamic equations, and validating results through Molecular Dynamics simulations.

Contribution

It provides a spectral analysis of the linearized Boltzmann operator and derives hydrodynamic equations for ballistic annihilation, a system with particle loss.

Findings

Spectral properties of the linearized Boltzmann operator characterized.

Hydrodynamic equations derived for coarse-grained fields.

Molecular Dynamics simulations confirm theoretical predictions.

Abstract

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.