Quantum manifestation of Lévy-type flights in a chaotic system

Chemical Physics

Volumn 284, Issue 1-2, 2002, Pages 3-11

  Iomin, A ^a   Zaslavsky, G M ^b,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b NEW YORK UNIVERSITY   (United States)

^c POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Accelerator mode islands; L vy type statistics; Quantum L vy type flights

Indexed keywords

ARTICLE; CHAOTIC DYNAMICS; FLIGHT; KINETICS; PROBABILITY; QUANTUM THEORY; STATISTICAL ANALYSIS; SURVIVAL; WAVEFORM;

EID: 0036829601     PISSN: 03010104     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0301-0104(02)00532-3     Document Type: Article

References (56)

1. E.W. Montroll, M.F. Shlesinger, in: J. Leibowitz, E. Montroll (Eds.), Studies in Statistical Mechanics, vol. 11, North-Holland, Amsterdam, 1984, p. 1.
2. J.P. Bouchand, A. Georges, Phys. Rep. 195 (1990) 127.
3. M.F. Shlesinger, G.M. Zaslavsky, U. Frisch (Eds.), Lévy Flights and Related Topics in Physics, Springer-Verlag, Heidelberg, 1995.
4. M.F. Shlesinger, G.M. Zaslavsky, J. Klafter, Nature 363 (1993) 31.
5. T. Geisel, in [3], p. 153.
6. J. Klafter, M.F. Shlesinger, G. Zumofen, Phys. Today 49 (1996) 33.
7. G. Zumofen, J. Klafter, in: R. Kutner, A. Pȩkalski, K. Sznajd-Weron (Eds.), Anomalous Diffusion, From Basic to Applications, Springer, Berlin, 1999.
8. R. Metzler, J. Klafter, Phys. Rep. 339 (2000) 1.
9. V. Afanasiev, R.Z. Sagdeev, G.M. Zaslavsky, Chaos 1 (1991) 143.
10. G.M. Zaslavsky, Physica D 76 (1994) 110; Chaos 4 (1994) 25.
11. G.M. Zaslavsky, Physica D 76 (1994) 110; Chaos 4 (1994) 25.
12. G.M. Zaslavsky, B.A. Niyazov, Phys. Rep. 283 (1997) 73.
13. P. Leboeuf, Physica D 116 (1998) 8; S.S. Abdullaev, K.H. Spatschek, Phys. Rev. E 60 (1999) R6287.
14. P. Leboeuf, Physica D 116 (1998) 8; S.S. Abdullaev, K.H. Spatschek, Phys. Rev. E 60 (1999) R6287.
15. G. Zimbardo, P. Veltri, P. Pommois, Phys. Rev. E 61 (2000) 1940.
16. J.D. Meiss et al., Physica D 6 (1983) 375.
17. J.D. Meiss, Phys. Rev. A 34 (1986) 2375; Rev. Mod. Phys. 64 (1992) 795.
18. J.D. Meiss, Phys. Rev. A 34 (1986) 2375; Rev. Mod. Phys. 64 (1992) 795.
19. V. Melnikov, in: S. Benkadda, F. Doveil, Y. Elskens (Eds.), Chaos, Transport, and Plasma Physics, World Scientific, Singapore, 1994, p. 126.
20. V. Rom-Kedar, G.M. Zaslavsky, Chaos 9 (1999) 6973.
21. G.M. Zaslavsky, M. Edelman, B.A. Niyazov, Chaos 7 (1997) 159.
22. B.V. Chirikov, D.L. Shepeliansky, Physica D 13 (1984) 395; B.V. Chirikov, Chaos, Solitons & Fractals 1 (1991) 79.
23. B.V. Chirikov, D.L. Shepeliansky, Physica D 13 (1984) 395; B.V. Chirikov, Chaos, Solitons & Fractals 1 (1991) 79.
24. G.M. Zaslavsky, M. Edelman, Chaos 10 (2000) 135; S. Benkadda, S. Kassibrakis, R. White, G. Zaslavsky, Phys. Rev. E 55 (1997) 4909; Phys. Rev. E 59 (1999) 3761.
25. G.M. Zaslavsky, M. Edelman, Chaos 10 (2000) 135; S. Benkadda, S. Kassibrakis, R. White, G. Zaslavsky, Phys. Rev. E 55 (1997) 4909; Phys. Rev. E 59 (1999) 3761.
26. G.M. Zaslavsky, M. Edelman, Chaos 10 (2000) 135; S. Benkadda, S. Kassibrakis, R. White, G. Zaslavsky, Phys. Rev. E 55 (1997) 4909; Phys. Rev. E 59 (1999) 3761.
27. D. Kusnezov, Phys. Rev. Lett. 72 (1994) 1990; D. Kusnezov, C.H. Lewenkopf, Phys. Rev. E 53 (1999) 2283.
28. D. Kusnezov, Phys. Rev. Lett. 72 (1994) 1990; D. Kusnezov, C.H. Lewenkopf, Phys. Rev. E 53 (1999) 2283.
29. D. Kusnezov, A. Bulgak, G.D. Dang, Phys. Rev. Lett. 82 (1999) 1136.
30. F. Bardou, J.P. Bouchaud, O. Emile, A. Aspect, C. Cohen-Tannoudji, Phys. Rev. Lett. 72 (1994) 203; B. Saubaméa, M. Leduc, C. Cohen-Tannoudji, Phys. Rev. Lett. 83 (1999) 3796.
31. F. Bardou, J.P. Bouchaud, O. Emile, A. Aspect, C. Cohen-Tannoudji, Phys. Rev. Lett. 72 (1994) 203; B. Saubaméa, M. Leduc, C. Cohen-Tannoudji, Phys. Rev. Lett. 83 (1999) 3796.
32. S. Schaufler, W.P. Schleich, V.P. Yakovlev, Phys. Rev. Lett. 83 (1999) 3162.
33. J.D. Hanson, E. Ott, T.M. Antonsen Jr., Phys. Rev. A 29 (1984) 819.
34. R. Roncaglia, L. Bonci, B.J. West, P. Grigolini, Phys. Rev. E 51 (1995) 5524; L. Bonci, P. Grigolini, A. Laux, R. Roncaglia, Phys. Rev. A 54 (1996) 112.
35. R. Roncaglia, L. Bonci, B.J. West, P. Grigolini, Phys. Rev. E 51 (1995) 5524; L. Bonci, P. Grigolini, A. Laux, R. Roncaglia, Phys. Rev. A 54 (1996) 112.
36. B. Sundaram, G.M. Zaslavsky, Phys. Rev. E 59 (1999) 7231.
37. A. Iomin, G.M. Zaslavsky, Chaos 10 (2000) 147.
38. A. Iomin, G.M. Zaslavsky, Phys. Rev. E 60 (1999) 7580.
39. Y.-C. Lai, R. Blümel, E. Ott, C. Grebogi, Phys. Rev. Lett. 68 (1992) 3491.
40. G. Casati, G. Maspero, D.L. Shepelyansky, Phys. Rev. Lett. 82 (2000) 524.
41. G. Casati, I. Guarneri, G. Maspero, Phys. Rev. Lett. 84 (2000) 63.
42. A. Buchleitner et al., Phys. Rev. Lett. 75 (1995) 3818.
43. G. Beneti, G. Casati, G. Maspero, D.L. Shepelyansky, Phys. Rev. Lett. 84 (2000) 4088.
44. R. Ketzmerick, Phys. Rev. B 54 (1996) 10841.
45. The fast Fourier transform is the standard build-in function of MATLAB package. Demanding to the runs is due to the sensitivity to numerical noise. Namely, the wave function is normalized to unity with the precision of 10 decimal digits after 1000 iterations.
46. A. Iomin, S. Fishman, Phys. Rev. Lett. 81 (1998) 1921; Physica D 131 (1999) 170.
47. A. Iomin, S. Fishman, Phys. Rev. Lett. 81 (1998) 1921; Physica D 131 (1999) 170.
48. B.G. Klappauf, W.H. Oskay, D.A. Steck, M.G. Raizen, Phys. Rev. Lett. 81 (1999) 4044.
49. A. Iomin, G.M. Zaslavsky, Phys. Rev. E 63 (2001) 047203.
50. A. Iomin, S. Fishman, G.M. Zaslavsky, Phys. Rev. E 65 (2002) 036215.
51. R. Artuso, M. Rusconi, Phys. Rev. E 64 (2001) 015204(R).
52. A. Buchleitner, K. Sacha, D. Delande, J. Zakrzewski, Eur. Phys. J. D 5 (1999) 145.
53. M. Stefancich et al., Phys. Rev. E 57 (1998) 6625.
54. P. Schlagheck, A. Buchleitner, Phys. Rev. A 63 (2001) 024701.
55. A. Krug, A. Buchleitner, Phys. Rev. Lett. 86 (2001) 3538.
56. T. Geisel, G. Radons, J. Rubner, Phys. Rev. Lett. 57 (1986) 2883.