Fine structure of distributions and central limit theorem in diffusive billiards

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 1, 2005, Pages

  Sanders, David P ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BILLIARD MODELS; FINE STRUCTURES; GAUSSIAN DENSITIES; LORENTZ GAS;

COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; NORMAL DISTRIBUTION; PARAMETER ESTIMATION; STATISTICAL MECHANICS; THEOREM PROVING; VELOCITY MEASUREMENT;

DIFFUSION;

EID: 41349088105     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.016220     Document Type: Article

References (45)

1. J. R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics (Cambridge University Press, Cambridge, 1999).
2. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer, Berlin, 1985).
3. R. Klages and J. R. Dorfman, Phys. Rev. E 59, 5361 (1999).
4. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
5. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, New York, 1992).
6. L. A. Bunimovich and Y. G. Sinai, Commun. Math. Phys. 78, 479 (1980/81).
7. L. A. Bunimovich, Y. G. Sinai, and N. I. Chernov, Russ. Math. Surveys 46, 47 (1991).
8. L. A. Bunimovich, in Hard Ball Systems and the Lorentz Gas, edited by D. Szász (Springer, Berlin, 2000), pp. 145-178.
9. P. L. Garrido and G. Gallavotti, J. Stat. Phys. 76, 549 (1994).
10. P. L. Garrido, J. Stat. Phys. 88, 807 (1997).
11. J. Machta and R. Zwanzig, Phys. Rev. Lett. 50, 1959 (1983).
12. R. Klages and C. Dellago, J. Stat. Phys. 101, 145 (2000).
13. D. P. Sanders (unpublished).
14. D. P. Sanders, Ph.D. thesis, Mathematics Institute, University of Warwick (2005).
15. N. Chernov and R. Markarian, Introduction to the Ergodic Theory of Chaotic Billiards (Institute de Matemática y Ciencias Afines, IMCA, Lima, 2001).
16. P. M. Bleher, J. Stat. Phys. 66, 315 (1992).
17. D. Szász and T. Varjú, e-print math.DS/0309357.
18. W. H. Press et al., Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992).
19. P. Gaspard, Chaos 3, 427 (1993).
20. D. Alonso, R. Artuso, G. Casati, and I. Guarneri, Phys. Rev. Lett. 82, 1859 (1999).
21. N. Chernov and L. S. Young, in Hard Ball Systems and the Lorentz Gas, edited by D. Szász (Springer, Berlin, 2000), pp. 89-120.
22. P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).
23. C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 101, 775 (2000).
24. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
25. T. J. Hunt and R. S. MacKay, Nonlinearity 16, 1499 (2003).
26. D. Alonso, A. Ruiz, and I. de Vega, Phys. Rev. E 66, 066131 (2002).
27. C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 103, 589 (2001).
28. X. P. Kong and E. G. D. Cohen, Phys. Rev. B 40, 4838 (1989).
29. A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise, 2nd ed. (Springer-Verlag, New York, 1994).
30. B. W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman & Hall, London, 1986).
31. D. W. Scott, Multivariate Density Estimation (Wiley, New York, 1992).
32. R. Klages, Deterministic Diffusion in One-Dimensional Chaotic Dynamical Systems (Wissenschaft und Technik Verlag, Berlin, 1996).
33. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
34. Y. Katznelson, An Introduction to Harmonic Analysis, 3rd ed. (Cambridge University Press, Cambridge, 2004).
35. R. Klages and N. Korabel, J. Phys. A 35, 4823 (2002).
36. F. Pène, Commun. Math. Phys. 225, 91 (2002).
37. B. Li, G. Casati, and J. Wang, Phys. Rev. E 67, 021204 (2003).
38. R. Klages, K. Rateitschak, and G. Nicolis, Phys. Rev. Lett. 84, 4268 (2000).
39. S. Wolfram, The Mathematica Book, 5th ed. (Wolfram Media, Champaign, IL, 2004).
40. A. Erdélyi et al., Higher Transcendental Functions. Vol. 1 (McGraw-Hill, New York, 1953).
41. R. Metzler and J. Klafter, Phys. Rep. 339, 77 (2000).
42. G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable: Theory and Technique (McGraw-Hill, New York, 1966).
43. H. van Beijeren, Physica D 193, 90 (2004).
44. G. Casati and T. Prosen, Phys. Rev. Lett. 83, 4729 (1999).
45. The author is indebted to Hernán Larralde for posing this question, and for the observation that the resulting position distribution may no longer be Gaussian.