Skip to main content

Chaos in Lorentz lattice gases

  • Conference paper
  • First Online:
25 Years of Non-Equilibrium Statistical Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 445))

Abstract

Lorentz lattice gases belong to the category of dynamical systems with positive Lyapunov exponents, and are therefore chaotic. We show using techniques from the kinetic theory of gases that these dynamical quantities can be computed explicitly.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.J. Evans, E.G.D. Cohen and G. Morris, Phys. Rev. A42, 5990 (1990); N.I. Chernov, G.L. Eyink, J.L. Lebowitz and Ya.G. Sinai, Phys. Rev. Lett. 10, 2209 (1993); Comm. Math. Phys. 154, 569 (1993).

    Google Scholar 

  2. P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990); P. Gaspard and F. Baras, in: Microscopic Simulations of Complex Hydrodynamic Phenomena, M. Maréschal and B.L. Holian, Eds. (Plenum Press, New York, 1992) p. 301.

    Google Scholar 

  3. J.R. Dorfman and P. Gaspard, Preprint, May 1994.

    Google Scholar 

  4. M.A. Shereshevsky, J. Nonlinear Science 2, 1 (1992).

    Google Scholar 

  5. F. Bognoli, R. Rechtman, and S. Ruffo, Physics Letters A172, 34 (1992); M. Cieplak, U. d'Ortona, D. Salin, R.B. Rybka, J.R. Banavar, Comput. Material Science 1, 87 (1992).

    Google Scholar 

  6. G.A. van Velzen, Lattice Lorentz Gases, Ph.D. Dissertation, University of Utrecht (1990); M.H. Ernst, in: Ordering Phenomena in Condensed Matter Physics; Z.M. Galasiewicz and A. Pekalski, Eds. (World Scientific, Singapore 1991), p. 291.

    Google Scholar 

  7. M.H. Ernst and G.A. van Velzen, J. Phys. A: Math. Gen. 22, 4327 (1989); J. Stat. Phys. 57, 455 (1989); A.J.H. Ossendrijver, A. Santos and M.H. Ernst, J. Stat. Phys. 71, 1015 (1993); H. van Beijeren and M.H. Ernst, J. Stat. Phys. 70, 793 (1993).

    Google Scholar 

  8. D. Frenkel, F. van Luyn and P.M. Binder, Europhys. Lett. 20, 7 (1992); P.M. Binder and D. Frenkel, Phys. Rev. A42, 2463 (1990); P.M. Binder, Phys. Rev. E49, R3565 (1994).

    Google Scholar 

  9. J.R. Dorfman, M.H. Ernst and D. Jacobs, preprint, June 1994.

    Google Scholar 

  10. E. Ott, Chaos in Dynamical Systems, (Cambridge Univ. Press, 1993); P. Walters, An Introduction to Ergodic Theory, (Sringer Verlag, Berlin 1992).

    Google Scholar 

  11. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems: An Introduction, (Cambridge University Press, Cambridge 1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. J. Brey J. Marro J. M. Rubí M. San Miguel

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag

About this paper

Cite this paper

Ernst, M.H., Dorfman, J.R. (1995). Chaos in Lorentz lattice gases. In: Brey, J.J., Marro, J., Rubí, J.M., San Miguel, M. (eds) 25 Years of Non-Equilibrium Statistical Mechanics. Lecture Notes in Physics, vol 445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59158-3_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-59158-3_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59158-0

  • Online ISBN: 978-3-540-49203-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics