Suppression and enhancement of diffusion in disordered dynamical systems

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

Volumn 65, Issue 5, 2002, Pages

  Klages, R ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; LYAPUNOV METHODS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; RANDOM PROCESSES;

CHAOTIC DIFFUSION; DISORDERED DYNAMICAL SYSTEMS; LORENTZ GASES; QUENCHED DISORDER;

CHAOS THEORY;

EID: 37649029832     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.055203     Document Type: Article

References (44)

1. G. Radons, MPIPKS Conference Proceedings, Dresden, 1998 (unpublished); see http://www.mpipks-dresden.mpg.de/~dds/
2. G. Radons, MPIPKS Conference Proceedings, Dresden, 1998 (unpublished); see http://www.mpipks-dresden.mpg.de/~dds/
3. G. Radons, Phys. Rev. Lett. 77, 4748 (1996); Adv. Solid State Phys. 38, 439 (1999).
4. G. Radons, Phys. Rev. Lett. 77, 4748 (1996); Adv. Solid State Phys. 38, 439 (1999).
5. J.W. Haus and K.W. Kehr, Phys. Rep. 150, 264 (1987); G.H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
6. J.W. Haus and K.W. Kehr, Phys. Rep. 150, 264 (1987); G.H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
7. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
8. K.W. Kehr, in Diffusion in Condensed Matter, edited by R.H. J. Kaerger and P. Heitjans (Vieweg, Braunschweig, 1998), pp. 265-305.
9. T. Geisel and J. Nierwetberg, Phys. Rev. Lett. 48, 7 (1982); M. Schell, S. Fraser, and R. Kapral, Phys. Rev. A 26, 504 (1982).
10. T. Geisel and J. Nierwetberg, Phys. Rev. Lett. 48, 7 (1982); M. Schell, S. Fraser, and R. Kapral, Phys. Rev. A 26, 504 (1982).
11. S. Grossmann and H. Fujisaka, Phys. Rev. A 26, 1779 (1982); Z. Phys. B: Condens. Matter 48, 261 (1982).
12. S. Grossmann and H. Fujisaka, Phys. Rev. A 26, 1779 (1982); Z. Phys. B: Condens. Matter 48, 261 (1982).
13. A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, 2nd ed., Applied Mathematical Sciences Vol. 38, (Springer, New York, 1992).
14. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998); P. Cvitanović et al., Classical and Quantum Chaos (Niels Bohr Institute, Copenhagen, 2001).
15. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998); P. Cvitanović et al., Classical and Quantum Chaos (Niels Bohr Institute, Copenhagen, 2001).
16. J.R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics (Cambridge University Press, Cambridge, 1999).
17. H. van Beijeren and J.R. Dorfman, Phys. Rev. Lett. 74, 4412 (1995); C. Dellago and H.A. Posch, Phys. Rev. E 52, 2401 (1995); H. van Beijeren, A. Latz, and J.R. Dorfman, ibid 57, 4077 (1998).
18. H. van Beijeren and J.R. Dorfman, Phys. Rev. Lett. 74, 4412 (1995); C. Dellago and H.A. Posch, Phys. Rev. E 52, 2401 (1995); H. van Beijeren, A. Latz, and J.R. Dorfman, ibid 57, 4077 (1998).
19. H. van Beijeren and J.R. Dorfman, Phys. Rev. Lett. 74, 4412 (1995); C. Dellago and H.A. Posch, Phys. Rev. E 52, 2401 (1995); H. van Beijeren, A. Latz, and J.R. Dorfman, ibid 57, 4077 (1998).
20. M.N. Popescu et al., Phys. Rev. E 58, R4057 (1998); Phys. Rev. Lett. 85, 3321 (2000); C.M. Arizmendi, F. Family, and A.L. Salas-Brito, Phys. Rev. E 63, 061104 (2001).
21. M.N. Popescu et al., Phys. Rev. E 58, R4057 (1998); Phys. Rev. Lett. 85, 3321 (2000); C.M. Arizmendi, F. Family, and A.L. Salas-Brito, Phys. Rev. E 63, 061104 (2001).
22. M.N. Popescu et al., Phys. Rev. E 58, R4057 (1998); Phys. Rev. Lett. 85, 3321 (2000); C.M. Arizmendi, F. Family, and A.L. Salas-Brito, Phys. Rev. E 63, 061104 (2001).
23. H.-C. Tseng and H.-J. Chen, Int. J. Mod. Phys. B 13, 83 (1999); 14, 643 (2000); H.-C. Tseng et al., Physica A 281, 323 (2000).
24. H.-C. Tseng and H.-J. Chen, Int. J. Mod. Phys. B 13, 83 (1999); 14, 643 (2000); H.-C. Tseng et al., Physica A 281, 323 (2000).
25. H.-C. Tseng and H.-J. Chen, Int. J. Mod. Phys. B 13, 83 (1999); 14, 643 (2000); H.-C. Tseng et al., Physica A 281, 323 (2000).
26. R. Artuso, Phys. Lett. A 160, 528 (1991); Physica D 76, 1 (1994); H.-C. Tseng et al., Phys. Lett. A 195, 74 (1994); C.-C. Chen, Phys. Rev. E 51, 2815 (1995).
27. R. Artuso, Phys. Lett. A 160, 528 (1991); Physica D 76, 1 (1994); H.-C. Tseng et al., Phys. Lett. A 195, 74 (1994); C.-C. Chen, Phys. Rev. E 51, 2815 (1995).
28. R. Artuso, Phys. Lett. A 160, 528 (1991); Physica D 76, 1 (1994); H.-C. Tseng et al., Phys. Lett. A 195, 74 (1994); C.-C. Chen, Phys. Rev. E 51, 2815 (1995).
29. R. Artuso, Phys. Lett. A 160, 528 (1991); Physica D 76, 1 (1994); H.-C. Tseng et al., Phys. Lett. A 195, 74 (1994); C.-C. Chen, Phys. Rev. E 51, 2815 (1995).
30. R. Klages and J.R. Dorfman, Phys. Rev. Lett. 74, 387 (1995); Phys. Rev. E 59, 5361 (1999).
31. R. Klages and J.R. Dorfman, Phys. Rev. Lett. 74, 387 (1995); Phys. Rev. E 59, 5361 (1999).
32. R. Klages, Deterministic Diffusion in One-Dimensional Chaotic Dynamical Systems (Wissenschaft & Technik-Verlag, Berlin, 1996).
33. R. Klages and J.R. Dorfman, Phys. Rev. E 55, R1247 (1997).
34. E. Barkai, V. Fleurov, and J. Klafter, Phys. Rev. E 61, 1164 (2000).
35. In the unperturbed case the numerical error is less than visible [15,16]. In case of perturbations, for each point a maximum of 1000 000 particles has been iterated up to 50 000 time steps each; representative error bars are included in all figures.
36. R. Zwanzig, J. Stat. Phys. 28, 127 (1982); B. Derrida, ibid, 31, 433 (1983); S.K. Lyo and P.M. Richards, Phys. Rev. B 32, 301 (1985).
37. R. Zwanzig, J. Stat. Phys. 28, 127 (1982); B. Derrida, ibid, 31, 433 (1983); S.K. Lyo and P.M. Richards, Phys. Rev. B 32, 301 (1985).
38. R. Zwanzig, J. Stat. Phys. 28, 127 (1982); B. Derrida, ibid, 31, 433 (1983); S.K. Lyo and P.M. Richards, Phys. Rev. B 32, 301 (1985).
39. Simulations have also been carried out for uniform disorder, Eq. (2), essentially yielding smoothed-out versions of the curves shown in Fig. 3.
40. R. Klages, Europhys. Lett. 57, 796 (2002).
41. Based on this heuristical argument, these phenomena have already been conjectured in Ref. [16], see p. 65.
42. K. Mussawisade, T. Wichmann, and K.W. Kehr, Surf. Sci. 4127 413, 55 (1998).
43. D. Weiss et al., Phys. Rev. Lett. 66, 2790 (1991).
44. R. Klages and C. Dellago, J. Stat. Phys. 101, 145 (2000).