Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems

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

Volumn 82, Issue 4, 2010, Pages

  Eberspächer, Alexander ^a   Main, Jörg ^a   Wunner, Günter ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

HARD-SPHERE; SCATTERING SYSTEMS; SEMICLASSICAL QUANTIZATION;

CHAOTIC SYSTEMS; FRACTAL DIMENSION; THREE DIMENSIONAL;

SPHERES;

EID: 78651302215     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.046201     Document Type: Article

References (35)

1. H. Weyl, Mathematische Annalen 71, 441 (1912). 10.1007/BF01456804
2. R. Courant, Math. Z. 7, 1 (1920). 10.1007/BF01199396
3. H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Bibliograph. Inst., Zürich, 1976).
4. J. Sjöstrand, Duke Math. J. 60, 1 (1990). 10.1215/S0012-7094-90- 06001-6
5. M. Zworski, Invent. Math. 136, 353 (1999). 10.1007/s002220050313
6. W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003). 10.1103/PhysRevLett.91.154101
7. K. K. Lin and M. Zworski, Chem. Phys. Lett. 355, 201 (2002). 10.1016/S0009-2614(02)00212-9
8. J. Wiersig and J. Main, Phys. Rev. E 77, 036205 (2008). 10.1103/PhysRevE.77.036205
9. J. A. Ramilowski, S. D. Prado, F. Borondo, and D. Farrelly, Phys. Rev. E 80, 055201 (2009). 10.1103/PhysRevE.80.055201
10. D. L. Shepelyansky, Phys. Rev. E 77, 015202 (2008). 10.1103/PhysRevE.77. 015202
11. M. Kopp and H. Schomerus, Phys. Rev. E 81, 026208 (2010). 10.1103/PhysRevE.81.026208
12. D. Sweet, E. Ott, and J. A. Yorke, Nature (London) 399, 315 (1999). 10.1038/20573
13. D. Sweet, B. W. Zeff, E. Ott, and D. P. Lathrop, Physica D 154, 207 (2001). 10.1016/S0167-2789(01)00235-4
14. Q. Chen, M. Ding, and E. Ott, Phys. Lett. A 145, 93 (1990). 10.1016/0375-9601(90)90198-W
15. A. E. Motter and P. S. Letelier, Phys. Lett. A 277, 18 (2000). 10.1016/S0375-9601(00)00674-5
16. K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Mathematics (Cambridge University Press, Cambridge, England, 1985), Vol. 85.
17. G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, Oxford, 2005).
18. M. Henseler, A. Wirzba, and T. Guhr, Ann. Phys. 258, 286 (1997). 10.1006/aphy.1997.5702
19. P. Gaspard and S. A. Rice, J. Chem. Phys. 90, 2255 (1989). 10.1063/1.456019
20. J. Main, E. Atilgan, H. S. Taylor, and G. Wunner, Phys. Rev. E 69, 056227 (2004). 10.1103/PhysRevE.69.056227
21. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York; Berlin; Heidelberg, 1990).
22. A. Voros, J. Phys. A 21, 685 (1988). 10.1088/0305-4470/21/3/023
23. M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley, Reading, MA, 2003).
24. P. Cvitanović, Phys. Rev. Lett. 61, 2729 (1988). 10.1103/PhysRevLett.61.2729
25. P. Cvitanović and B. Eckhardt, Phys. Rev. Lett. 63, 823 (1989). 10.1103/PhysRevLett.63.823
26. R. Artuso, E. Aurell, and P. Cvitanović, Nonlinearity 3, 325 (1990). 10.1088/0951-7715/3/2/005
27. A. Wirzba, Phys. Rep. 309, 1 (1999). 10.1016/S0370-1573(98)00036-2
28. H. Primack and U. Smilansky, Phys. Rep. 327, 1 (2000). 10.1016/S0370-1573(99)00093-9
29. M. Sieber, Nonlinearity 11, 1607 (1998). 10.1088/0951-7715/11/6/010
30. P. Cvitanovic and B. Eckhardt, Nonlinearity 6, 277 (1993). 10.1088/0951-7715/6/2/008
31. M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995). 10.1063/1.468999
32. J. Main, Phys. Rep. 316, 233 (1999). 10.1016/S0370-1573(98)00131-8
33. Dž. Belkić, P. A. Dando, J. Main, and H. S. Taylor, J. Chem. Phys. 113, 6542 (2000). 10.1063/1.1310612
34. P. Gaspard and S. A. Rice, J. Chem. Phys. 90, 2225 (1989). 10.1063/1.456017
35. K. Pance, W. Lu, and S. Sridhar, Phys. Rev. Lett. 85, 2737 (2000). 10.1103/PhysRevLett.85.2737