Lorentz Gas with Thermostatted Walls

Annales Henri Poincare

Volumn 11, Issue 6, 2010, Pages 1117-1169

  Chernov, Nikolai ^a   Dolgopyat, Dmitry ^b  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

^b Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78349254570     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-010-0047-2     Document Type: Article

References (31)

1. Alves J., Bonatti C., Viana M.: SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Invent. Math. 140, 351-398 (2000).
2. Baladi V., Gouëzel S.: Good Banach spaces for piecewise hyperbolic maps via interpolation. Ann. Inst. H. Poincaré 26, 1453-1481 (2009).
3. Baladi V., Gouëzel S.: Banach spaces for piecewise cone hyperbolic maps. J. Modern Dyn. 4, 91-137 (2010).
4. Bonetto F., Daems D., Lebowitz J. L.: Properties of stationary nonequilibrium states in the thermostatted periodic Lorentz gas. I. The one particle system. J. Stat. Phys. 101, 35-60 (2000).
5. Brin M., Stuck G.: Introduction to Dynamical Systems. Cambridge University Press, Cambridge (2002).
6. Bunimovich L. A., Sinai Ya. G.: Statistical properties of Lorentz gas with periodic configuration of scatterers. Comm. Math. Phys. 78, 479-497 (1980/81).
7. Bunimovich L. A., Sinai Ya. G., Chernov N. I.: Statistical properties of two-dimensional hyperbolic billiards. Russ. Math. Surv. 46, 47-106 (1991).
8. Chernov N.: Decay of correlations and dispersing billiards. J. Stat. Phys. 94, 513-556 (1999).
9. Chernov N.: Sinai billiards under small external forces. Ann. H. Poincaré 2, 197-236 (2001).
10. Chernov N.: A stretched exponential bound on time correlations for billiard flows. J. Stat. Phys. 127, 21-50 (2007).
11. Chernov N.: Sinai billiards under small external forces II. Ann. H. Poincaré 9, 91-107 (2008).
12. Chernov N., Dolgopyat D.: Brownian Brownian motion-I. Memoirs AMS 198(927), 193 (2009).
13. Chernov N., Dolgopyat D.: Galton board: limit theorems and recurrence. J. Am. Math. Soc. 22, 821-858 (2009).
14. Chernov, N., Dolgopyat, D.: Diffusive motion and recurrence on an idealized Galton Board. Phys. Rev. Lett. 99, paper 030601 (2007).
15. Chernov N., Dolgopyat D.: Anomalous current in periodic Lorentz gases with infinite horizon. Russ. Math. Surv. 64, 73-124 (2009).
16. Chernov N., Dolgopyat D.: Particle's drift in self-similar billiards. Ergod. Theory Dyn. Syst. 28, 389-403 (2008).
17. Chernov, N., Markarian, R.: Chaotic billiards. Mathematical Surveys and Monographs, vol. 127, pp. xii+316. AMS Publishing Providence, RI (2006).
18. Chernov N. I., Eyink G. L., Lebowitz J. L., Sinai Ya. G.: Steady-state electrical conduction in the periodic Lorentz gas. Comm. Math. Phys. 154, 569-601 (1993).
19. Chernov N. I., Eyink G. L., Lebowitz J. L., Sinai Ya. G.: Derivation of Ohm's law in a deterministic mechanical model. Phys. Rev. Lett. 70, 2209-2212 (1993).
20. Chernov N., Zhang H.-K.: Billiards with polynomial mixing rates. Nonlineartity 4, 1527-1553 (2005).
21. Dettmann C. P., Morriss G. P.: Crisis in the periodic Lorentz gas. Phys. Rev. E. 54, 4782-4790 (1996).
22. Kornfeld I. P., Fomin S. V., Sinai Ya. G.: Ergodic Theory. Springer, New York (1982).
23. Gallavotti G., Ornstein D.: Billiards and Bernoulli schemes. Comm. Math. Phys. 38, 83-101 (1974).
24. Galton, F.: Natural Inheritance. MacMillan (1889) (facsimile available at http://www. galton. org).
25. Lorentz H. A.: The motion of electrons in metallic bodies. Proc. Amst. Acad. 7, 438-453 (1905).
26. Melbourne I., Török A.: Statistical limit theorems for suspension flows. Israel J. Math. 144, 191-209 (2004).
27. Moran B., Hoover W.: Diffusion in a periodic Lorentz gas. J. Stat. Phys. 48, 709-726 (1987).
28. Ruelle D.: A review of linear response theory for general differentiable dynamical systems. Nonlinearity 22, 855-870 (2009).
29. Sinai Ya. G.: Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards. Russ. Math. Surv. 25, 137-189 (1970).
30. Szász D., Varjú T.: Limit Laws and Recurrence for the Planar Lorentz Process with Infinite Horizon. J. Stat. Phys. 129, 59-80 (2007).
31. Young L.-S.: Statistical properties of dynamical systems with some hyperbolicity. Ann. Math. 147, 585-650 (1998).