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Computationally efficient method to construct scar functions

F. Revuelta1, E. G. Vergini1,2, R. M. Benito1, and F. Borondo3,*

  • 1Grupo de Sistemas Complejos and Departamento de Física, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, E-28040 Madrid, Spain
  • 2Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina
  • 3Departamento de Química, and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain

  • *f.borondo@uam.es
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Phys. Rev. E 85, 026214 – Published 24 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.026214

Abstract

The performance of a simple method [E. L. Sibert III, E. Vergini, R. M. Benito, and F. Borondo, New J. Phys. 10, 053016 (2008)] to efficiently compute scar functions along unstable periodic orbits with complicated trajectories in configuration space is discussed, using a classically chaotic two-dimensional quartic oscillator as an illustration.

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References (36)

  1. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer Verlag, New York, 1990).
  2. A. Einstein, Verh. Dtsch. Phys. Ges. 19, 82 (1917).
  3. A. D. Stone, Phys. Today 58(8), 37 (2005).
  4. M. C. Gutzwiller, J. Math. Phys. 11, 1791 (1970).
  5. E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
  6. E. J. Heller, in Chaos and Quantum Physics, edited by M. J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam, 1991).
  7. L. Kaplan and E. J. Heller, Ann. Phys. (NY) 264, 171 (1998).
  8. E. B. Bogomolny, Physica D 31, 169 (1988).
  9. M. V. Berry, Proc. R. Soc. London A 423, 219 (1989).
  10. S. Tomsovic and E. J. Heller, Phys. Rev. Lett. 70, 1405 (1993); S. Tomsovic and J. H. Lefebvre, ibid. 79, 3629 (1997).
  11. D. A. Wisniacki, E. Vergini, R. M. Benito, and F. Borondo, Phys. Rev. E 70, 035202(R) (2004); Phys. Rev. Lett. 94, 054101 (2005); 97, 094101 (2006).
  12. J. P. Keating and S. D. Prado, Proc. R. Soc. London A 457, 1855 (2001).
  13. D. Wisniacki and G. G. Carlo, Phys. Rev. E 77, 045201(R) (2008); M. Novaes, J. M. Pedrosa, D. Wisniacki, G. G. Carlo, and J. P. Keating, ibid. 80, 035202(R) (2009).
  14. H. J. Stöckman, Quantum Chaos. An Introduction (Cambridge University Press, Cambridge, UK, 2000).
  15. S. Sridhar, Phys. Rev. Lett. 67, 785 (1991); J. Stein and H. Stöckmann, ibid. 68, 2867 (1992).
  16. P. B. Wilkinson et al., Nature (London) 380, 608 (1996); R. Akis, D. K. Ferry, and J. P. Bird, Phys. Rev. Lett. 79, 123 (1997).
  17. J. U. Nöckel and A. D. Stone, Nature (London) 385, 45 (1997); C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998); S.-B. Lee, J.-H. Lee, J.-S. Chang, H.-J. Moon, S. W. Kim, and K. An, Phys. Rev. Lett. 88, 033903 (2002); T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, Phys. Rev. E 67, 015207(R) (2003); Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010); J. Wiersig, A. Eberspächer, J.-B. Shim, J.-W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, Phys. Rev. A 84, 023845 (2011).
  18. V. Doya, O. Legrand, F. Mortessagne, and C. Miniatura, Phys. Rev. Lett. 88, 014102 (2001); C. Michel, V. Doya, O. Legrand, and F. Mortessagne, ibid. 99, 224101 (2007).
  19. L. Huang, Y.-C. Lai, D. K. Ferry, S. M. Goodnick, and R. Akis, Phys. Rev. Lett. 103, 054101 (2009).
  20. G. G. de Polavieja, F. Borondo, and R. M. Benito, Phys. Rev. Lett. 73, 1613 (1994).
  21. E. G. Vergini, J. Phys. A 33, 4709 (2000); E. G. Vergini and G. G. Carlo, ibid. 33, 4717 (2000).
  22. E. G. Vergini and G. G. Carlo, J. Phys. A 34, 4525 (2001); G. G. Carlo, E. G. Vergini, and P. Lustemberg, ibid. 35, 7965 (2001).
  23. A. Vagov, H. Schomerus, and V. V. Zalipaev, Phys. Rev. E 80, 056202 (2009).
  24. E. J. Heller, P. W. O’Connor, and J. Gehlen, Phys. Scr. 40, 354 (1989).
  25. E. L. Sibert III, E. Vergini, R. M. Benito, and F. Borondo, New J. Phys. 10, 053016 (2008).
  26. E. G. Vergini, E. L. Sibert III, F. Revuelta, F. Borondo, and R. M. Benito, Europhys. Lett. 89, 40013 (2009).
  27. R. L. Waterland, J.-M. Yuan, C. C. Martens, R. E. Gillilan, and W. P. Reinhardt, Phys. Rev. Lett. 61, 2733 (1988); C. C. Martens et al., J. Chem. Phys. 90, 2328 (1989); B. Eckhardt, G. Hose, and E. Pollak, Phys. Rev. A 39, 3776 (1989); O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rep. 223, 44 (1993).
  28. P. Dahlqvist and G. Russberg, Phys. Rev. Lett. 65, 2837 (1990).
  29. E. J. Heller, J. Chem. Phys. 65, 4979 (1976).
  30. R. G. Littlejohn, Phys. Rep. 138, 195 (1986).
  31. V. Maslov and M. Fedoriuk, Semiclassical Approximation in Quantum Mechanics (Reidel, Dordrecht, 1981).
  32. S. C. Creagh, J. M. Robbins, and R. G. Littlejohn, Phys. Rev. A 42, 1907 (1990); J. M. Robbins, Nonlinearity 4, 343 (1991).
  33. Notice that all considered POs present no TPs.
  34. M. Brack and R. M. Bhaduri, Semiclassical Physics (Addison-Wesley, Reading, 1997).
  35. E. Vergini, D. M. Schneider, and A. M. F. Rivas, J. Phys. A 41, 405102 (2008).
  36. F. Revuelta, R. M. Benito, F. Borondo, and E. Vergini (unpublished).

Outline

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Phys. Rev. E 85, 026214– Published 24 February, 2012
  • Received 15 November 2011

©2012 American Physical Society

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