- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Finite-size fluctuations in interacting particle systems

E. Ben-Naim*

P. L. Krapivsky†

  • Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachussets 02215, USA

  • *Electronic address: ebn@lanl.gov
  • †Electronic address: paulk@bu.edu
PDF

Phys. Rev. E 69, 046113 – Published 28 April, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.046113

Abstract

Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of particles Nf scales logarithmically with the system size N, Nf∼lnN. Statistical fluctuations, that become significant as the number of particles diminishes, are responsible for this behavior. This phenomenon underlies a broad range of interacting particle systems including in particular multispecies annihilation processes.

View figure in article

Article Text

References (30)

  1. P. Ehrenfest and T. Ehrenfest, Phys. Z. 8, 311 (1907); P. Erenfest and T. Erenfest, Enzyklopädie der Mathematischen Wissenschaften (Berlin, 1911), Vol. IV, p. 32.
  2. F. Kohlrausch and E. Schrödinger, Phys. Z. 27, 306 (1926).
  3. M. Kac, Probability and Related Topics in Physical Sciences (Interscience, London, 1959).
  4. F. Ritort, Phys. Rev. Lett. 75, 1190 (1995); S. Franz and F. Ritort, J. Phys. A 30, L359 (1997).
  5. C. Godrèche, J. P. Bouchaud, and M. Mezard, J. Phys. A 28, L603 (1995).
  6. C. Godrèche and J. M. Luck, J. Phys. A 29, 1915 (1996); 30, 6245 (1997); 32, 6033 (1999).
  7. P. Bialas, Z. Burda, and D. Johnson, Nucl. Phys. B 493, 505 (1997); 542, 413 (1999).
  8. N. L. Johnson and S. Kotz, Urn Models and their Applications (Wiley, New York, 1977).
  9. S. Kotz, H. Mahmoud, and P. Robert, Stat. Probab. Lett. 49, 163 (2000).
  10. P. Flajolet, J. Cabarro, and H. Pekari (unpublished).
  11. K. Sigmund, Games of Life (Oxford University Press, Oxford, 1993).
  12. A. Bagchi and A. K. Pal, SIAM J. Algebraic Discrete Methods 6, 394 (1985).
  13. D. Aldous, B. Flannery, and J. L. Palacios, Prob. Eng. Infor. Sci. 2, 293 (1988).
  14. F. Eggenberger and G. Pólya, Z. Angew. Math. Mech. 3, 279 (1923).
  15. A. A. Lushnikov, J. Colloid Interface Sci. 65, 276 (1977).
  16. J. L. Spouge, J. Colloid Interface Sci. 107, 38 (1985).
  17. P. G. J. van Dongen and M. H. Ernst, J. Stat. Phys. 49, 879 (1987).
  18. P. L. Krapivsky and S. Redner, J. Phys. A 35, 9517 (2002).
  19. P. L. Krapivsky and S. Redner, Phys. Rev. Lett. 89, 258703 (2002).
  20. E. Ben-Naim and P. L. Krapivsky Europhys. Lett.65, 151 (2004).
  21. J. D. Murray, Mathematical Biology (Springer-Verlag, New York, 1989).
  22. The official rock-paper-scissors web page: http://www.worldrps.com/.
  23. B. Kerr, M. A. Riley, M. W. Feldman, and B. J. M. Bhannan, Nature (London) 418, 171 (2002).
  24. J. Hofbauer and K. Sigmund, Bull., New Ser., Am. Math. Soc. 40, 479 (2003).
  25. S. Redner, A Guide to Fisrt Passage Processes (Cambridge, New York, 2001).
  26. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North Holland, Amsterdam, 2003).
  27. D. ben-Avraham and S. Redner, Phys. Rev. A 34, 501 (1986).
  28. O. Deloubriere, H. J. Hilhorst, and U. C. Tauber, Phys. Rev. Lett. 89, 250601 (2002).
  29. D. X. Zhong, R. Dawkins, and D. ben-Avraham, Phys. Rev. E 67, 040101 (2003).
  30. E. Ben-Naim, L. Frachebourg, and P. L. Krapivsky, Phys. Rev. E 53, 3078 (1996).

Outline

Information

Phys. Rev. E 69, 046113– Published 28 April, 2004
  • Received 19 December 2003

© 2004 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation