# Search for universality in one-dimensional ballistic annihilation kinetics

Source: [Search for universality in one-dimensional ballistic annihilation kinetics](<https://www.sota2.com/research/paper/68fa246d2c2a3760193a3f62>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:10:57.035Z

Authors: Pierre-Antoine Rey, Michel Droz, Jaroslaw Piasecki

Published: 1997-08-19T12:29:07.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9708138>)

[PDF](<https://arxiv.org/pdf/cond-mat/9708138.pdf>)