Classical scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

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

Volumn 68, Issue 4 2, 2003, Pages 462071-462078

  Emmanouilidou, A ^a   Jung, C ^b   Reichl, L E ^c  

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

^b INSTITUTO DE CIENCIAS FÍSICAS   (Mexico)

^c UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; ENTROPY; FRACTALS; MATRIX ALGEBRA; SET THEORY; THERMODYNAMICS; TOPOLOGY; TREES (MATHEMATICS);

CHAOTIC INVARIANT SETS; GAUSSIAN POTENTIAL; TRANSFER MATRICES;

ELECTRON SCATTERING;

EID: 0346934973     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. L.E. Reichl, The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, Berlin, 1983).
2. J.N. Bardsley and M.J. Comellsa, Phys. Rev. A 39, 2252 (1989).
3. G. Yao and S.-I. Chu, Phys. Rev. A 45, 6735 (1992).
4. M. Marinescu and M. Gavrila, Phys. Rev. A 53, 2513 (1996).
5. T. Timberlake and L.E. Reichl, Phys. Rev. A 64, 033404 (2001).
6. A. Emmanouilidou and L.E. Reichl, Phys. Rev. A 65, 033405 (2002).
7. B. Eckhardt, Physica D 33, 89 (1988); U. Smilansky, in Proceedings of Les Hauches Summer School, edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1989), pp. 371-441; E. Ott and T. Tél, Chaos 3, 417 (1993); Z. Kovács and L. Wiesenfeld, Phys. Rev. E 51, 5476 (1995).
8. B. Eckhardt, Physica D 33, 89 (1988); U. Smilansky, in Proceedings of Les Hauches Summer School, edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1989), pp. 371-441; E. Ott and T. Tél, Chaos 3, 417 (1993); Z. Kovács and L. Wiesenfeld, Phys. Rev. E 51, 5476 (1995).
9. B. Eckhardt, Physica D 33, 89 (1988); U. Smilansky, in Proceedings of Les Hauches Summer School, edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1989), pp. 371-441; E. Ott and T. Tél, Chaos 3, 417 (1993); Z. Kovács and L. Wiesenfeld, Phys. Rev. E 51, 5476 (1995).
10. B. Eckhardt, Physica D 33, 89 (1988); U. Smilansky, in Proceedings of Les Hauches Summer School, edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1989), pp. 371-441; E. Ott and T. Tél, Chaos 3, 417 (1993); Z. Kovács and L. Wiesenfeld, Phys. Rev. E 51, 5476 (1995).
11. C. Jung and H.J. Scholz, J. Phys. A 20, 3607 (1987); T. Tél Phys. Rev. A 36, 1502 (1987).
12. C. Jung and H.J. Scholz, J. Phys. A 20, 3607 (1987); T. Tél Phys. Rev. A 36, 1502 (1987).
13. P. Cvitanović, G. Gunaratne, and I. Procaccia, Phys. Rev. A 38, 1503 (1988); D. Auerbach and I. Procaccia, ibid, 41, 6602 (1990); C. Jung and P. Richter, J. Phys. A 23, 2847 (1990); G. Troll, Physica D 50, 276 (1991); J. Vollmer and W. Breymann, Helv. Phys. Acta 66, 91 (1993).
14. P. Cvitanović, G. Gunaratne, and I. Procaccia, Phys. Rev. A 38, 1503 (1988); D. Auerbach and I. Procaccia, ibid, 41, 6602 (1990); C. Jung and P. Richter, J. Phys. A 23, 2847 (1990); G. Troll, Physica D 50, 276 (1991); J. Vollmer and W. Breymann, Helv. Phys. Acta 66, 91 (1993).
15. P. Cvitanović, G. Gunaratne, and I. Procaccia, Phys. Rev. A 38, 1503 (1988); D. Auerbach and I. Procaccia, ibid, 41, 6602 (1990); C. Jung and P. Richter, J. Phys. A 23, 2847 (1990); G. Troll, Physica D 50, 276 (1991); J. Vollmer and W. Breymann, Helv. Phys. Acta 66, 91 (1993).
16. P. Cvitanović, G. Gunaratne, and I. Procaccia, Phys. Rev. A 38, 1503 (1988); D. Auerbach and I. Procaccia, ibid, 41, 6602 (1990); C. Jung and P. Richter, J. Phys. A 23, 2847 (1990); G. Troll, Physica D 50, 276 (1991); J. Vollmer and W. Breymann, Helv. Phys. Acta 66, 91 (1993).
17. P. Cvitanović, G. Gunaratne, and I. Procaccia, Phys. Rev. A 38, 1503 (1988); D. Auerbach and I. Procaccia, ibid, 41, 6602 (1990); C. Jung and P. Richter, J. Phys. A 23, 2847 (1990); G. Troll, Physica D 50, 276 (1991); J. Vollmer and W. Breymann, Helv. Phys. Acta 66, 91 (1993).
18. B. Rückerl and C. Jung, J. Phys. A 27, 55 (1994).
19. C. Beck and F. Schlogel, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, U.K., 1993), Secs. 8.4 and 17.5.
20. G. Karolyi and T. Tél, Phys. Rep. 290, 125 (1997).
21. M.J. Feigenbaum, M.H. Jensen, and I. Procaccia, Phys. Rev. Lett. 57, 1503 (1986).
22. H.A. Kramers, Collected Scientific Papers (Amsterdam, North-Holland, 1956), p. 272.
23. W.C. Henneberger, Phys. Rev. Lett. 21, 838 (1968).
24. A.S. Fearnide, R.M. Portvliege, and R. Shakeshaft, Phys. Rev. A 51, 1471 (1995).
25. S. Smale, Bull. Am. Math. Soc. 73, 747 (1967).
26. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, U.K., 1993).
27. C. Jung, C. Lipp, and T.H. Seligman, Ann. Phys. (N.Y.) 275, 151 (1999).
28. D. Bigie, A. Leonard, and S. Wiggins, Nonlinearity 4, 775 (1991).
29. B. Rückerl and C. Jung, J. Phys. A 27, 6741 (1994).
30. W. Breymann and C. Jung, Europhys. Lett. 25, 509 (1994).