A note on the Ruelle pressure for a dilute disordered Sinai billiard

Journal of Statistical Physics

Volumn 108, Issue 5-6, 2002, Pages 767-785

  Van Beijeren, H ^a,b   Dorfman, J R ^c  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c Bldg 142   (United States)

Author keywords

Ruelle pressure; Sinai billiard

Indexed keywords

EID: 0141561927     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019860925625     Document Type: Article

References (22)

1. Ya. G. Sinai, Gibbs measures in Ergodic theory, Russian Math. Surveys 27:21 (1972).
2. D. Ruelle, Thermodynamic Formalism (Addison Wesley, New York, 1978).
3. R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Vol. 470 (Springer-Verlag, Berlin, 1975).
4. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, UK, 1998).
5. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1993).
6. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, Cambridge, 1995).
7. C. Appert, H. van Beijeren, M. H. Ernst, and J. R. Dorfman, The thermodynamic formalism in the thermodynamic limit: Diffusive systems with static disorder, Phys. Rev. E 54:R1013 (1996).
8. C. Appert, H. van Beijeren, M. H. Ernst, and J. R. Dorfman, Thermodynamic formalism and localization in Lorentz gases and hopping models, J. Stat. Phys. 87:1253 (1997).
9. I. M. Lifshitz, Energy spectrum of disordered systems, Adv. Phys. 13, 483 (1964).
10. R. Griffiths, Nonanalytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett. 23:17 (1969).
11. M. Donsker and S. R. S. Varadhan, Asymptotics for the Wiener sausage, Comm. Pure Appl. Math. 28:525 (1975); ibid 32:721 (1979).
12. M. Donsker and S. R. S. Varadhan, Asymptotics for the Wiener sausage, Comm. Pure Appl. Math. 28:525 (1975); ibid 32:721 (1979).
13. Ya. G. Sinai, Dynamical systems with elastic reflections, Russian Math. Surveys, 25:137 (1970).
14. N. I. Chernov, Decay of correlations and dispersing billiards, J. Stat. Phys. 94:513 (1999).
15. H. van Beijeren and J. R. Dorfman, Lyapunov exponents and KS entropy for the Lorentz gas at low densities, Phys. Rev. Lett. 74:4412 (1995).
16. H. van Beijeren, A. Latz, and J. R. Dorfman, Chaotic properties of dilute two- and three-dimensional random Lorentz gases I: Equilibrium systems, Phys. Rev. E 57:4077 (1998).
17. D. Burago, S. Ferleger, and A. Kononenko, Topological entropy of semi-dispersing billiards, Ergodic Theory Dynam. Systems 18:791 (1998).
18. J. Machta and R. Zwanzig, Diffusion in a periodic Lorentz gas, Phys. Rev. Lett. 50:1959 (1983).
19. P. Gaspard and F. Baras, Chaotic scattering and diffusion in the Lorentz gas, Phys. Rev. E 51:5332 (1995).
20. E. J. Heller, Bound state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits, Phys. Rev. Lett. 53:1515 (1984).
21. H. van Beijeren, J. R. Dorfman, H. A. Posch, and C. Dellago, Kolmogorov-Sinai entropy for dilute gases in equilibrium, Phys. Rev. E 56:5272 (1997).
22. P. N. Pusey and W. van Megen, Observation of a glass transition in suspensions of spherical colloidal particles, Phys. Rev. Lett. 59:2083 (1987).