https://doi.org/10.1140/epjb/s10051-021-00258-w
Colloquium - Statistical and Nonlinear Physics
Ballistic annihilation in one dimension: a critical review
1
Departamento de Física, Universidad de Guadalajara, Jalisco, Guadalajara, Mexico
2
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
3
Centro de Ciencias Físicas, Cuernavaca, Morelos, Mexico
a
soham.biswas@academicos.udg.mx
Received:
16
November
2021
Accepted:
25
November
2021
Published online:
8
December
2021
In this article, we review the problem of reaction annihilation 
on a real lattice in one dimension, where A particles move ballistically in one direction with a discrete set of possible velocities. We first discuss the case of pure ballistic annihilation, that is a model in which each particle moves simultaneously at constant speed. We then review ballistic annihilation with superimposed diffusion in one dimension. This model consists of diffusing particles each of which diffuses with a fixed bias, which can be either positive or negative with probability 1/2, and annihilate upon contact. When the initial concentration of left- and right-moving particles is same, the concentration c(t) decays as 
with time, for pure ballistic annihilation. However, when the diffusion is superimposed decay is faster and the concentration 
. We also discuss the nearest-neighbor distance distribution as well as crossover behavior.
The original online version of this article was revised to delete a typesetting comment that has been left in the article: “query Please provide an explanation as to why there is no data or why the data will not be deposited. Your explanation will be displayed as ‘Authors’ comment’.”.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
