IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v94y2021i12d10.1140_epjb_s10051-021-00258-w.html
   My bibliography  Save this article

Ballistic annihilation in one dimension: a critical review

Author

Listed:
  • Soham Biswas

    (Universidad de Guadalajara)

  • Francois Leyvraz

    (Universidad Nacional Autónoma de México
    Centro de Ciencias Físicas)

Abstract

In this article, we review the problem of reaction annihilation $$A+A \rightarrow \emptyset $$ A + A → ∅ 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 $$t^{-1/2}$$ t - 1 / 2 with time, for pure ballistic annihilation. However, when the diffusion is superimposed decay is faster and the concentration $$c(t) \sim t^{-3/4}$$ c ( t ) ∼ t - 3 / 4 . We also discuss the nearest-neighbor distance distribution as well as crossover behavior. Graphical Abstract

Suggested Citation

  • Soham Biswas & Francois Leyvraz, 2021. "Ballistic annihilation in one dimension: a critical review," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-10, December.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:12:d:10.1140_epjb_s10051-021-00258-w
    DOI: 10.1140/epjb/s10051-021-00258-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-021-00258-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/s10051-021-00258-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Foong, S. K. & Kanno, S., 1994. "Properties of the telegrapher's random process with or without a trap," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 147-173, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.
    2. Iacus, Stefano Maria, 2001. "Statistical analysis of the inhomogeneous telegrapher's process," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 83-88, November.
    3. Cinque, Fabrizio & Orsingher, Enzo, 2021. "On the exact distributions of the maximum of the asymmetric telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 601-633.
    4. Nikita Ratanov, 2020. "First Crossing Times of Telegraph Processes with Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 349-370, March.
    5. Iuliano, Antonella & Macci, Claudio, 2023. "Asymptotic results for the absorption time of telegraph processes with a non-standard barrier at the origin," Statistics & Probability Letters, Elsevier, vol. 196(C).
    6. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
    7. Kolesnik, Alexander D. & Turbin, Anatoly F., 1998. "The equation of symmetric Markovian random evolution in a plane," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 67-87, June.
    8. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
    9. Igor G. Pospelov & Stanislav A. Radionov, 2015. "Optimal Dividend Policy When Cash Surplus Follows The Telegraph Process," HSE Working papers WP BRP 48/FE/2015, National Research University Higher School of Economics.
    10. Ratanov, Nikita, 2021. "On telegraph processes, their first passage times and running extrema," Statistics & Probability Letters, Elsevier, vol. 174(C).
    11. Cinque, Fabrizio, 2022. "A note on the conditional probabilities of the telegraph process," Statistics & Probability Letters, Elsevier, vol. 185(C).
    12. Bogachev, Leonid & Ratanov, Nikita, 2011. "Occupation time distributions for the telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1816-1844, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:94:y:2021:i:12:d:10.1140_epjb_s10051-021-00258-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.