Dynamics of Annihilation II: Fluctuations of Global Quantities

TL;DR

This paper develops a theoretical framework to predict fluctuations and correlations in a ballistic annihilation gas, validated by simulations, advancing understanding of non-equilibrium statistical mechanics.

Contribution

It introduces a hydrodynamic approach to analyze fluctuations in ballistic annihilation, linking microscopic dynamics to macroscopic observables with explicit predictions.

Findings

Predictions match Molecular Dynamics and Monte-Carlo simulations

Explicit formulas for fluctuations of particle number, momentum, and energy

Cross-correlations between global quantities are characterized

Abstract

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.