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Evolution of classical projected phase space density in billiards

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Abstract

The classical phase space density projected on to the configuration space offers a means of comparing classical and quantum evolution. In this alternate approach that we adopt here, we show that for billiards, the eigenfunctions of the coarse-grained projected classical evolution operator are identical to a first approximation to the quantum Neumann eigenfunctions. Moreover, there exists a correspondence between the respective eigenvalues although their time evolutions differ.

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References

  1. A Lasota and M MacKey,Chaos, fractals, and noise;stochastic aspects of dynamics (Springer-Verlag, Berlin, 1994)

    Google Scholar 

  2. P Gaspard,Chaos, scattering and statistical mechanics (Cambridge University Press, 1998)

  3. M Pollicott,Invent. Math. 81, 413 (1985)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. D Ruelle,Phys. Rev. Lett. 56, 405 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  5. M Sano,Phys. Rev. E59, R3795 (1999)

    MathSciNet  ADS  Google Scholar 

  6. D Braun,Chaos 9, 730 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. C Manderfeld, J Weber and F Haake,J. Phys. A34, 9893 (2001)

    MathSciNet  ADS  Google Scholar 

  8. S Nonnenmacher,Nonlinearity 16, 1685 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. R R Puri,Mathematical methods of quantum optics (Springer, Berlin, 2001)

    MATH  Google Scholar 

  10. W Zhang, D Feng and R Gilmore,Rev. Mod. Phys. 62, 867 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  11. T A Driscoll and H P W Gottlieb,Phys. Rev. E68, 016702 (2003)

    MathSciNet  ADS  Google Scholar 

  12. H-J Stockmann,Quantum chaos — An introduction (Cambridge University Press, Cambridge, 1999)

    Google Scholar 

  13. J L Vega, T Uzer and J Ford,Phys. Rev. E48, 3414 (1993)

    MathSciNet  ADS  Google Scholar 

  14. D Biswas,Phys. Rev. E61, 5073 (2000)

    ADS  Google Scholar 

  15. D Biswas,Phys. Rev. E67, 026208 (2003)

    ADS  Google Scholar 

  16. The degree of polygonalization depends on the de Broglie wavelength, λ; see [12]

  17. D Biswas,Phys. Rev. E61, 5129 (2000)

    ADS  Google Scholar 

  18. D Biswas,Phys. Rev. E63, 016213 (2001)

    ADS  Google Scholar 

  19. D Biswas,Phys. Rev. Lett. 93, 204102 (2004)

    Article  ADS  Google Scholar 

  20. D Biswas and S Sinha,Phys. Rev. Lett. 70, 916 (1993)

    Article  ADS  Google Scholar 

  21. D Biswas,Phys. Rev. E54, R1044 (1996)

    ADS  Google Scholar 

  22. E J Heller,Phys. Scr. 40, 354 (1989)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. J L Vega, T Uzer and J Ford,Phys. Rev. E52, 1490 (1995)

    MathSciNet  ADS  Google Scholar 

  24. D Biswas and S Sinha,Phys. Rev. E60, 408 (1999)

    MathSciNet  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Theoretical Physics Division, Bhabha Atomic Research Centre, 400 085, Mumbai, India

    Debabrata Biswas

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  1. Debabrata Biswas
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Biswas, D. Evolution of classical projected phase space density in billiards. Pramana - J Phys 64, 563–575 (2005). https://doi.org/10.1007/BF02706204

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