Quantum chaos in a ripple billiard

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

Volumn 65, Issue 5, 2002, Pages

  Li, Wenjun ^a   Reichl, L E ^a   Wu, Biao ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM CHAOS; QUANTUM SYSTEMS; RIPPLE BILLIARDS; WIGNER DISTRIBUTIONS;

EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; FUNCTIONS; HAMILTONIANS; MATHEMATICAL MODELS; MATRIX ALGEBRA; QUANTUM THEORY; STATISTICAL METHODS;

CHAOS THEORY;

EID: 41349094589     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.056220     Document Type: Article

References (31)

1. L. E. Reichl, The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, Berlin, 1992).
2. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1990).
3. E. J. Heller and S. Tomsovic, Phys. Today 46 (7), 38 (1993).
4. E.J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
5. G.A. Luna-Acosta, Kyungsun Na, L.E. Reichl, and A. Khrokhin Phys. Rev. E 53, 3271 (1996).
6. Gursoy B. Akguc and L.E. Reichl, J. Stat. Phys. 98, 813 (2000).
7. O. Bohigas, M. Giannoni, and Schmit, Phys. Rev. Lett. 52, l (1984).
8. F. Izrailev, Phys. Rev. Lett. 56, 541 (1986).
9. H.D. Graf, H.L. Harney, H. Lengeler, C.H. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt, and H. Weidenmuller, Phys. Rev. Lett. 69, 1296 (1992).
10. H. Alt, C. Dembowski, H.D. Graf, R. Hofferbert, H. Rehfeld, A. Richter, and C. Schmit, Phys. Rev. E 60, 2851 (1999).
11. P.B. Wilkinson, T.M. Fromhold, L. Eaves, F.W. Sheard, N. Miura, and T. Takamasu, Nature (London) 380, 608 (1996); T.M. Fromhold, P.B. Wilkinson, L. Eaves, F.W. Sheard, P.C. Main, M. Henini, M.J. Carter, N. Miura, and T. Takamasu, Chaos Solitons Fractals 8, 1381 (1997).
12. P.B. Wilkinson, T.M. Fromhold, L. Eaves, F.W. Sheard, N. Miura, and T. Takamasu, Nature (London) 380, 608 (1996); T.M. Fromhold, P.B. Wilkinson, L. Eaves, F.W. Sheard, P.C. Main, M. Henini, M.J. Carter, N. Miura, and T. Takamasu, Chaos Solitons Fractals 8, 1381 (1997).
13. V. Milner, J.L. Hanssen, W.C. Campbell, and M.G. Raizen, Phys. Rev. Lett. 86, 1514 (2001); F.L. Moore, J.C. Robinson, C. Bharucha, P.E. Williams, and M.G. Raizen, ibid. 73, 2974 (1994); N. Friedman, A. Kaplan, D. Carsso, and N. Davidson, ibid. 86, 1518 (2001).
14. V. Milner, J.L. Hanssen, W.C. Campbell, and M.G. Raizen, Phys. Rev. Lett. 86, 1514 (2001); F.L. Moore, J.C. Robinson, C. Bharucha, P.E. Williams, and M.G. Raizen, ibid. 73, 2974 (1994); N. Friedman, A. Kaplan, D. Carsso, and N. Davidson, ibid. 86, 1518 (2001).
15. V. Milner, J.L. Hanssen, W.C. Campbell, and M.G. Raizen, Phys. Rev. Lett. 86, 1514 (2001); F.L. Moore, J.C. Robinson, C. Bharucha, P.E. Williams, and M.G. Raizen, ibid. 73, 2974 (1994); N. Friedman, A. Kaplan, D. Carsso, and N. Davidson, ibid. 86, 1518 (2001).
16. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, and S.S.M. Wong, Rev. Mod. Phys. 53, 385 (1981); T. Terasaka and T. Matsushita, Phys. Rev. A 32, 538 (1985).
17. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, and S.S.M. Wong, Rev. Mod. Phys. 53, 385 (1981); T. Terasaka and T. Matsushita, Phys. Rev. A 32, 538 (1985).
18. B. C. Brookes and W. F. L. Dick, Introduction to Statistical Method (Heinemann, London, 1969); S. L. Meyer, Data Analysis for Scientists and Engineers (Wiley, New York, 1975).
19. B. C. Brookes and W. F. L. Dick, Introduction to Statistical Method (Heinemann, London, 1969); S. L. Meyer, Data Analysis for Scientists and Engineers (Wiley, New York, 1975).
20. F. Borgonovi, G. Casati, and B. Li, Phys. Rev. Lett. 77, 4744 (1996).
21. K.M. Frahm and D.L. Shepelyansky, Phys. Rev. Lett. 78, 1440 (1997).
22. E. Haller, H. Koppel, and L. Cederbaum, Chem. Phys. Lett. 101, 215 (1983); R. Venkataraman, J. Phys. B 15, 4293 (1982).
23. E. Haller, H. Koppel, and L. Cederbaum, Chem. Phys. Lett. 101, 215 (1983); R. Venkataraman, J. Phys. B 15, 4293 (1982).
24. These eigenstates fit quite well to a Bohr-Sommerfeld-like quantization condition; kD=j(2π) + φ, where k is the wave vector, D is the length of a periodic orbit, j is expected to be an integer, ad the periodic orbit associated Malsov phase φ is a constant, which can be obtained from the eigenenergies of periodic orbit scarred states discussed in this paper. See also Ref. [11]
25. S. W. McDonald, Lawrence Berkeley Laboratory Report No. LBL-14837, 1983 (unpublished).
26. S. Sridhar and E.J. Heller, Phys. Rev. A 46, R1728 (1992).
27. W. Chism, T. Timberlake, and L.E. Reichl, Phys. Rev. E 58, 1713 (1998).
28. T. Timberlake and L.E. Reichl, Phys. Rev. A 59, 2886 (1999).
29. F. Simonotti, E. Vergini, and M. Saraceno, Phys. Rev. E 56, 3859 (1997).
30. P.B. Umbanhowar, F. Melo, and H.L. Swinney, Nature (London) 382, 793 (1996).
31. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 246 (1940).