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.
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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).
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.
J.R. Dorfman and P. Gaspard, Preprint, May 1994.
M.A. Shereshevsky, J. Nonlinear Science 2, 1 (1992).
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).
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.
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).
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).
J.R. Dorfman, M.H. Ernst and D. Jacobs, preprint, June 1994.
E. Ott, Chaos in Dynamical Systems, (Cambridge Univ. Press, 1993); P. Walters, An Introduction to Ergodic Theory, (Sringer Verlag, Berlin 1992).
C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems: An Introduction, (Cambridge University Press, Cambridge 1993).
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© 1995 Springer-Verlag
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Ernst, M.H., Dorfman, J.R. (1995). Chaos in Lorentz lattice gases. In: Brey, J.J., Marro, J., RubÃ, 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
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DOI: https://doi.org/10.1007/3-540-59158-3_44
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