Kinetics of ballistic annihilation and branching

Details Kinetics of ballistic annihilation and branching Kinetics of ballistic annihilation and branching

1998-08-25

arxiv.org/abs/cond-mat/9808278v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also avaiable at http://mykonos.unige.ch/~rey/pubt.html

Scientific paper

10.1103/PhysRevE.59.126

We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each moving particle can spontaneously generate an offspring having the same velocity as its mother with probability 1-q. This model is solved analytically in mean-field approximation and studied by numerical simulations. It is found that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the slow dynamics of the system is governed by the coarsening of clusters of particles having the same velocities, while for q>1/2 the system relaxes rapidly towards its stationary state characterized by a distribution of small cluster sizes.

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