Brownian motion under annihilation dynamics

M. I. Garcia de Soria 1, P. Maynar 2, 3, E. Trizac 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 78 (2008) 061110

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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Laboratoire de Physique Théorique d'Orsay (LPT),
    CNRS : UMR8627 – Université Paris XI - Paris Sud
  • 3. Fisica Teorica, Universidad de Sevilla,
    Universidad de Sevilla