Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas

Journal of Statistical Physics

Volumn 88, Issue 1-2, 1997, Pages 81-103

  Matsuoka, H ^a   Martin Jr , R F ^a  

^a ILLINOIS STATE UNIVERSITY   (United States)

Author keywords

Billiards; Chaos; Diffusion coefficients; Ergodic theory; Long time tails; Periodic Lorentz gas; Velocity autocorrelation functions

Indexed keywords

EID: 0031184697     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02508465     Document Type: Article

References (23)

1. Ya. G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Russ. Math. Surveys 25:137 189 (1970) for the periodic Lorentz gas with a bounded horizon. I. Kubo, Billiard Problem. Seminar on Probability 37 (1972) (in Japanese) , and Lect. Notes in Math. 330:287 (1973) for the periodic Lorentz gas with an unbounded horizon.
2. Ya. G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Russ. Math. Surveys 25:137 189 (1970) for the periodic Lorentz gas with a bounded horizon. I. Kubo, Billiard Problem. Seminar on Probability 37 (1972) (in Japanese) , and Lect. Notes in Math. 330:287 (1973) for the periodic Lorentz gas with an unbounded horizon.
3. Ya. G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Russ. Math. Surveys 25:137 189 (1970) for the periodic Lorentz gas with a bounded horizon. I. Kubo, Billiard Problem. Seminar on Probability 37 (1972) (in Japanese) , and Lect. Notes in Math. 330:287 (1973) for the periodic Lorentz gas with an unbounded horizon.
4. G. Gallavotti and D. S. Ornstein, Billiards and Bernoulli schemes. Commun. Math. Phys. 38:83-101 (1974).
5. L. A. Bunimovich and Ya. G. Sinai, Statistical properties of Lorentz gas with periodic configuration of scatterers, Commun. Math. Phys. 78:479-197 (1981). L. A. Bunimovich, Ya. G. Sinai, and N. I. Chernov, Statistical properties of two-dimensional hyperbolic billiards, Russ. Math. Surveys 46:47-106 (1991).
6. L. A. Bunimovich and Ya. G. Sinai, Statistical properties of Lorentz gas with periodic configuration of scatterers, Commun. Math. Phys. 78:479-197 (1981). L. A. Bunimovich, Ya. G. Sinai, and N. I. Chernov, Statistical properties of two-dimensional hyperbolic billiards, Russ. Math. Surveys 46:47-106 (1991).
7. G. Casati, G. Comparin, and I. Guarneri, Decay of correlations in certain hyperbolic systems, Phys. Rev. A 26:717-719 (1982).
8. P. L. Garrido and G. Gallavotti. Billiards correlation functions, J. Stat. Phys. 76:549-585 (1994).
9. J. Machta and B. Reinhold, Decay of correlations in the regular Lorentz gas, J. Stat. Phys. 42:949-959 (1986).
10. J. Machta, Power law decay of correlations in a billiard problem, J. Stat. Phys. 32:555-564 (1983).
11. F. Vivaldi, G. Casati, and I. Guarneri, Origin of long-time tails in strongly chaotic systems, Phys. Rev. Lett. 51:727-730 (1983).
12. J.-P. Bouchaud and P. Le Doussal, Numerical study of a d-dimensional periodic Lorentz gas with universal properties. J. Stat. Phys. 41:225-248 (1985).
13. J.-P. Bouchaud and P. Le Doussal, Critical behaviour and intermittency in Sinai's billiard, Physica D 20:335-349 (1986).
14. B. Friedman and R. F. Martin Jr., Decay of the velocity autocorrelation function for the periodic Lorentz gas, Phys. Lett. A 105:23-26 (1984).
15. B. Friedman. The billiard problem, PhD. Thesis, University of Illinois, Physics Department (1985).
16. B. Friedman and R. F. Martin Jr., Behavior of the velocity autocorrelation function for the periodic Lorentz gas, Physica D 30:219-227 (1988).
17. J. Machta and R. Zwanzig, Diffusion in a periodic gas, Phys. Rev. Lett. 50:1959 (1983).
18. L. A. Bunimovich, Decay of correlations in dynamical systems with chaotic behavior, Zh. Eksp. Teor. Fiz. 89:1452-1471 (1985) (Sov. Phys. JETP 62:842-852 (1986)).
19. L. A. Bunimovich, Decay of correlations in dynamical systems with chaotic behavior, Zh. Eksp. Teor. Fiz. 89:1452-1471 (1985) (Sov. Phys. JETP 62:842-852 (1986)).
20. P. M. Bleher, Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon, J. Stat. Phys. 66:315-373 (1992).
21. A. Zacherl, T. Geisel, J. Nierwetberg, and G. Radons, Power spectra for anomalous diffusion in the extended Sinai billiard, Phys. Lett. A 114:317-321 (1986).
22. N. I. Chernov, Statistical properties of the periodic Lorentz gas. Multidimensional case, J. Stat. Phys. 74:11-53 (1994).
23. C. P. Lowe and A. J. Masters, The long-time behaviour of the velocity autocorrelation function in a Lorentz gas, Physica A 195:149 (1993).