Search for universality in one-dimensional ballistic annihilation kinetics

Details Search for universality in one-dimensional ballistic annihilation kinetics Search for universality in one-dimensional ballistic annihilation kinetics

1997-08-19

arxiv.org/abs/cond-mat/9708138v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, needs multicol, epsf and revtex. 8 postscript figures included. Submitted to Phys. Rev. E. Also avaiable at http://

Scientific paper

10.1103/PhysRevE.57.138

We study the kinetics of ballistic annihilation for a one-dimensional ideal gas with continuous velocity distribution. A dynamical scaling theory for the long time behavior of the system is derived. Its validity is supported by extensive numerical simulations for several velocity distributions. This leads us to the conjecture that all the continuous velocity distributions \phi(v) which are symmetric, regular and such that \phi(0) does not vanish, are attracted in the long time regime towards the same Gaussian distribution and thus belong to the same universality class. Moreover, it is found that the particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.

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