Pramana

, Volume 76, Issue 1, pp 37–45 | Cite as

Application of Lie transform perturbation method for multidimensional non-Hermitian systems

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Abstract.

Three-dimensional non-Hermitian systems are investigated using classical perturbation theory based on Lie transformations. Analytic expressions for total energy in terms of action variables are derived. Both real and complex semiclassical eigenvalues are obtained by quantizing the action variables. It was found that semiclassical energy eigenvalues calculated with the classical perturbation theory are in very good agreement with exact energies and for certain non-Hermitian systems second-order classical perturbation theory performed better than the second-order Rayleigh–Schroedinger perturbation theory.

Keywords.

Classical perturbation theory; non-Hermitian quantum mechanics; Birkhoff normal forms. 

PACS Nos

03.65.Sq; 03.65.-W 
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References

  1. [1]
    G Hori, Publ. Astron. Soc. Japan 18, 287 (1966)ADSGoogle Scholar
  2. [2]
    G Hori, Publ. Astron. Soc. Japan 19, 229 (1967)ADSGoogle Scholar
  3. [3]
    R Ramaswamy and R Marcus, J. Chem. Phys. 74, 1385 (1981)MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    R Ramaswamy and R Marcus, J. Chem. Phys. 74, 1379 (1981)MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    C M Bender and S Boettcher, Phys. Rev. Lett. 80, 5243 (1998)MathSciNetADSMATHCrossRefGoogle Scholar
  6. [6]
    E Delabaere and F Pham, Phys. Lett. A250, 25, 29 (1998)Google Scholar
  7. [7]
    C M Bender, S Boettcher and P N Meisinger, J. Math. Phys. 40, 2201 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  8. [8]
    C M Bender, F Cooper, P N Meisinger and V M Savage, Phys. Lett. A259, 224 (1999)MathSciNetADSGoogle Scholar
  9. [9]
    C M Bender and G V Dunne, J. Math. Phys. 40, 4616 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    C M Bender, D C Brody and H F Jones, Phys. Rev. Lett. 89, 270401 (2002)MathSciNetCrossRefGoogle Scholar
  11. [11]
    A Nanayakkara, Czech. J. Phys. 54, 101 (2004); J. Phys. A: Math. Gen. 37, 4321 (2004)Google Scholar
  12. [12]
    A Nanayakkara, J. Phys. A: Math. Gen. 37, 4321 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  13. [13]
    C M Bender, S Boettcher and P N Meisinger, J. Math. Phys. 40, 2201 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  14. [14]
    C M Bender, J Chen, D W Darg and K A Milton, J. Phys. A: Math. Gen. 39, 4219 (2006)MathSciNetADSMATHCrossRefGoogle Scholar
  15. [15]
    C M Bender and D W Darg, J. Math. Phys. 48, 042703 (2007)MathSciNetCrossRefGoogle Scholar
  16. [16]
    C M Bender, G V Dunne, P N Meisinger and M Simsek, Phys. Lett. A281, 311 (2001)MathSciNetADSGoogle Scholar
  17. [17]
    A Mostafazadeh, Phys. Lett. A357, 177 (2006)MathSciNetADSGoogle Scholar
  18. [18]
    C L Siegel and J L Moser, Lectures on celestial mechanics (Springer-Verlag, Berlin, 1971)MATHCrossRefGoogle Scholar
  19. [19]
    G D Birkhoff, Acta Math. 43, 1 (1922)MathSciNetCrossRefGoogle Scholar
  20. [20]
    W Easter and R A Marcus, J. Chem. Phys. 61, 4301 (1974)ADSCrossRefGoogle Scholar
  21. [21]
    D W Noid and R A Marcus, J. Chem. Phys. 67, 559 (1977)ADSCrossRefGoogle Scholar
  22. [22]
    D W Noid, M L Koszykowski and R A Marcus, J. Chem. Phys. 67, 404, 4301 (1977)Google Scholar

Copyright information

© Indian Academy of Sciences 2011

Authors and Affiliations

  1. 1.Institute of Fundamental StudiesKandySri Lanka

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