Chaos, pseudochaos, and quantum chaos in non-equilibrium statistical mechanics

Acta Physica Polonica B

Volumn 37, Issue 9, 2006, Pages 2463-2502

  Dorfman, J R ^a  

^a Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; MICROSCOPIC EXAMINATION; PHASE EQUILIBRIA; QUANTUM THEORY; RANDOM PROCESSES; STATISTICAL MECHANICS;

EQUILIBRIUM STATES; LYAPUNOV EXPONENTS; MICROSCOPIC DYNAMICS; PSEUDOCHAOS;

CHAOS THEORY;

EID: 33748785758     PISSN: 05874254     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (67)

1. P. Gaspard. Chaos, Scattering, and Statistical Mechanics, Cambridge University Press, Cambridge 1998.
2. J.R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics, Cambridge University Press, Cambridge 1999.
3. W.G. Hoover, Time Reversibility, Computer Simulation, and Chaos, World Scientific, Singapore 1999.
4. D.J. Evans, G.P. Morriss, Statistical Mechanics of Non-equilibrium Liquids, Academic Press, London 1990.
5. M.A. Nielson, I.L. Chuang, Quantum Computation and Quantum Information Cambridge University Press, Cambridge 2000.
6. M. Srednicki, J. Phys. A 32, 1163 (1999).
7. C.P. Dettmann, E.G.D. Cohen, J. Stat. Phys. 101, 775 (2000);
8. J. Stat. Phys. 103, 589 (2001).
9. G.M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford 2005.
10. D. Wojcik, J.R. Dorfman, Phys. Rev. E66, 036110 (2002);
11. Phys. Rev. Lett. 90, 230602 (2003);
12. Physica D 187, 223 (2004).
13. V.I. Arnold, A. Avez. Ergodic Problems of Classical Mechanics, W.A. Benjamin, Inc., New York 1968.
14. P. Walters. Ergodic Theory, Springer-Verlag, New York 1981.
15. A. Katok, B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge 1995.
16. E. Hopf, Ergodentheorie, Ergebnisse der Mathematik und ihrer Grenagebiete, Bd. 2, 5 (1948).
17. Hard Ball Systems and the Lorentz Gas, ed. D. Szasz, Springer Verlag, Berlin 2000.
18. arc, 05-348, 2005, and references therein.
19. D. Turaev, V. Rom-Kedar, Nonlinearity 11, 575 (1998);
20. Physica D 130, 187 (1999).
21. M. Berry, Hamiltonian Dynamical Systems eds. R.S. MacKay, J.D. Meiss, Adam Hilger, Bristol, England 1987.
22. J.R. Dorfman, H. van Beijeren, Statistical Mechanics, Part B ed. B. Berne, Plenum Press, New York 1977, p. 65.
23. D.V. Anosov, Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature, in Proceedings of the Steklov Institute of Mathematics, volume 90, Providence 1967.
24. G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995);
25. G. Gallavotti, E.G.D. Cohen, J. Stat. Phys. 80, 931 (1995).
26. N.N. Bogoliubov, Studies in Statistical Mechanics, volume 1, North Holland Publishing Co., Amsterdam 1962, p. 5.
27. P. Gaspard, G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).
28. J.R. Dorfman, P. Gaspard, Phys. Rev. E51, 28 (1995).
29. P. Gaspard, J. Stat. Phys. 89, 1215 (1997).
30. J.R. Dorfman, P. Gaspard, T. Gilbert, Phys. Rev. E66, 026110 (2002).
31. D.J. Evans, D.J. Searles, Adv. Phys. 51, 1529 (2002), and references therein.
32. G. Crooks, Phys. Rev. E60, 2721 (1999);
33. Phys. Rev. E61, 2361 (2000).
34. L.P. Kadanoff, C. Tang. Proc. Nat. Acad. Sci., USA 81, 1276 (1984).
35. H. Kantz, P. Grassberger, Physica D, 17, 75 (1985).
36. D. Ruelle, J.-P. Eckmann. Rev. Mod. Phys. 57, 617 (1985).
37. P. Gaspard, F. Baras. Phys. Rev. E51, 5332 (1995).
38. S. Viscardy, P. Gaspard, Phys. Rev. E68, 041204 (2003);
39. Phys. Rev. E68, 041205 (2003).
40. R. van Zon, H. van Beijeren, J.R. Dorfman, Kinetic theory estimates for the Kolmogorov-Sinai Entropy, and the Largest Lyapunov Exponents for Dilute, Hard Ball Gases, and for Dilute, Random Lorentz Gases, in Hard Ball Systems and the Lorentz Gas, ed. D. Szasz, op.cit..
41. L.-S. Young, Ergodic. Th. Dyn. Sys. 2, 109 (1982).
42. T. Gilbert, J.R. Dorfman, P. Gaspard, Nonlinearity 14, 339 (2001).
43. P. Gaspard, I. Claus, T. Gilbert, J.R. Dorfman, Phys. Rev. Lett. 86, 1506 (2001).
44. H.A. Posch, W.G. Hoover, Phys. Rev. A39, 2175 (1989);
45. Phys. Rev. E49, 1913 (1994).
46. L. Barreira, Y. Pesin, Lyapunov Exponents and Smooth Ergodic Theory, American Mathematical Society, Providence 2001.
47. S. Tasaki, T. Gilbert, J.R. Dorfman, Chaos 8, 424 (1998).
48. D.J. Evans, E.G.D. Cohen, G.P. Morriss, Phys. Rev. A42, 5990 (1990).
49. Ch. Dellago, H.A. Posch, W.G. Hoover, Phys. Rev. E53, 1485 (1996);
50. Ch. Dellago, H.A. Posch, Phys. Rev. E55, R9 (1997).
51. C.P. Dettmann, G.P. Morriss. Phys. Rev. E53, R5545 (1996).
52. T. Gilbert, J.R. Dorfman, P. Gaspard, Phys. Rev. Lett. 85, 1606 (2000).
53. D.J. Evans, E.G.D. Cohen, G.P. Morriss. Phys. Rev. Lett. 71, 2401 (1993).
54. S. Tabachnikov, Billiards, Panoramas et Synthéses, Société Mathématique de France, Paris 1995.
55. A. Einstein, Zum quantensatz von Sommerfeld und Epstein, Verhandlungen der Deutsch. Physikal. Gesell. 19, 82, (1917).
56. H-J. Stöckmann, Quantum Chaos: An Introduction, Cambridge University Press, Cambridge 1999.
57. F. Haake, Quantum Signatures of Chaos, 2nd. Ed., Springer Verlag, Berlin 2001.
58. M.V. Berry, Quantum Chaology, in J. Al-Khalili, Quantum: A Guide for the Perplexed, Weidenfeld and Nicolson, London 2003.
59. M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer-Verlag, New York 1990.
60. A.I. Shnirelman, The KAM Theory and Asymptotics of the Spectrum of Elliptic Operators, ed. V.F. Lasutkin, Springer Verlag, Berlin 1991.
61. M.L. Mehta, Random Matrices, Academic Press, New York 1991.
62. O. Bohigas, M.J. Gianonni, C. Schmidt, Phys. Rev. Lett. 52, 1 (1984).
63. S. Müller, S. Heusler, P. Braun, F. Haake, A. Altland, Phys. Rev. Lett. 93, 014103 (2004).
64. A. Goussev, J.R. Dorfman, Phys. Rev. E71, 026225 (2005).
65. N.L. Balazs, A. Voros, Ann. Phys. 190, 1 (1989).
66. M. Saraceno, Ann. Phys. 199, 37 (1989).
67. R. Alicki, M. Fannes, Quantum Dynamical Systems, Oxford University Press, Oxford 2001.