Brownian motion under annihilation dynamics

TL;DR

This paper studies the motion of a heavy particle in a bath of particles undergoing ballistic annihilation, deriving a Fokker-Planck equation, analyzing its diffusive behavior, and confirming results with simulations.

Contribution

It introduces a Fokker-Planck framework for a tagged particle in ballistic annihilation dynamics, revealing unique diffusive properties and temperature differences.

Findings

Velocity distribution approaches Gaussian with a different temperature.

Mean squared displacement grows exponentially over time.

Analytical results match Monte Carlo simulations.

Abstract

The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding diffusive behavior are worked out. In the long time limit, the intruder velocity distribution function approaches a Gaussian form, but with a different temperature from its bath counterpart. As a consequence of the continuous decay of particles in the bath, the mean squared displacement increases exponentially in the collision per particle time scale. Analytical results are finally successfully tested against Monte Carlo numerical simulations.