Long-time-tail effects on Lyapunov exponents of a random, two-dimensional field-driven Lorentz gas

Journal of Statistical Physics

Volumn 100, Issue 1-2, 2000, Pages 279-311

  Panja, D ^a   Dorfman, J R ^a   Van Beijeren, Henk ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

BBGKY hierarchy equations; Extended Lorentz Boltzmann equation; Long time tail effect; Lorentz gas; Lyapunov exponents

Indexed keywords

EID: 0034342452     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018604115227     Document Type: Article

References (29)

1. D. J. Evans and G. P. Morriss, Statistical Mechanics of Non-equilibrium Liquids (Academic Press, London, 1990).
2. D. J. Evans, W. G. Hoover, B. H. Failor, B. Moran, and A. J. C. Ladd, Nonequilibrium molecular dynamics via Gauss's principle of least constraint. Phys. Rev. A 28:1016 (1983).
3. D. J. Evans, Computer "experiment" for nonlinear thermodynamics of Couette flow, J. Chem. Phys. 78:3297 (1983).
4. N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Ya. G Sinai, Steady-state electrical conduction in periodic Lorentz gas. Comm. Math. Phys. 154:569 (1993).
5. C. Dettmann, The Lorentz gas: A paradigm for non-equilibrium stationary states, preprint.
6. H. van Beijeren and J. R. Dorfman, Lyapunov exponents and Kolmogorov-Sinai entropy for the Lorentz gas at low densities, Phys. Rev. Lett. 74:4412 (1995).
7. H. van Beijeren, A. Latz, and J. R. Dorfman, Chaotic properties of dilute two-and three-dimensional random Lorentz gases: Equilibrium systems, Phys. Rev. E 57:4077 (1998).
8. H. van Beijeren, J. R. Dorfman, E. G. D. Cohen, H. A. Posch, and Ch. Dellago, Lyapunov exponents from kinetic theory for a dilute, field-driven Lorentz gas, Phys. Rev. Lett. 77:1974 (1996).
9. A. Latz, H. van Beijeren, and J. R. Dorfman, Lyapunov spectrum and the conjugate pairing rule for a thermostatted random Lorentz gas: Kinetic theory. Phys. Rev. Lett. 78:207 (1997).
10. J. R. Dorfman and H. van Beijeren, Statistical Mechanics, Part B. Time-Dependent Processes, Bruce H. Berne, ed. (Plenum Press, New York, 1977).
11. M. H. Ernst and A. Weijland. Long time behaviour of the velocity auto-correlation function in a Lorentz gas. Phys. Lett. 34A:39 (1971).
12. Ya. G. Sinai, Dynamical systems with elastic rellections. Ergodic properties of dispersing Billiards. Russ. Math. Surv. 25:137 (1970).
13. Z. Kovács, private discussion.
14. Z. Kovács, Orbit stability in billiards in magnetic field, Phys. Rep. 290:49 (1997).
15. W. G. Hoover, Computational Statistical Mechanics (Elsevier Science Publishers, Amsterdam, 1991).
16. D. Panja, An elementary proof of Lyapunov exponent pairing for hard-sphere systems at constant kinetic energy, preprint.
17. J. R. Dorfman, An Introduction to Chaos in Non-Equilibrium Statistical Mechanics (Cambridge Univ. Press, 1999).
18. D. Panja and J. R. Dorfman, unpublished.
19. J. R. Dorfman and M. H. Ernst, Hard-sphere binary collision operators, J. Stat. Phys. 57:581 (1989). See also M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen, Hard-sphere dynamics and binary-collision operators. Physica 45:127 (1969).
20. J. R. Dorfman and M. H. Ernst, Hard-sphere binary collision operators, J. Stat. Phys. 57:581 (1989). See also M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen, Hard-sphere dynamics and binary-collision operators. Physica 45:127 (1969).
21. J. M. J. van Leeuwen and A. Weijland, Non-analytic density behaviour of the diffusion coefficient of a Lorentz gas, Physica 36:457 (1967). See also C. Bruin, A computer experiment on diffusion in the Lorentz gas, Physica 72:261 (1974).
22. J. M. J. van Leeuwen and A. Weijland, Non-analytic density behaviour of the diffusion coefficient of a Lorentz gas, Physica 36:457 (1967). See also C. Bruin, A computer experiment on diffusion in the Lorentz gas, Physica 72:261 (1974).
23. M. H. Ernst and J. R. Dorfman, Nonanalytic dispersion relations in classical fluids. I. The hard sphere gas, Physica 61:157 (1972).
24. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, 1970).
25. H. Kruis, Masters thesis, University of Utrecht, The Netherlands (1997).
26. J. R. Dorfman, A. Latz, and H. van Beijeren, Bogoliubov-Born Green-Kirkwood-Yvon hierarchy methods for sums of Lyapunov exponents for Dilute gases, Chaos 8:444 (1998).
27. H. A. Posch and Ch. Dellago. Lyapunov spectrum and the conjugate pairing rule for a thermostatted random Lorentz gas: Numerical simulations, Phys. Rev. Lett. 78:211 (1997).
28. A. Latz, H. van Beijeren, and J. R. Dorfman, Chaotic properties of dilute two-and three-dimensional random Lorentz gases II: Open systems, preprint.
29. D. Panja, Ph.D. thesis, University of Maryland, College Park, USA (2000).