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An Influence Functional Approach for the Elimination of Variables in Stochastic Processes

  • Horacio S. Wio

Abstract

We present a non-adiabatic scheme for the elimination of variables in stochastic processes, based on the “influence functional” method of Feynman. Particularly, the case of multivariate Fokker-Planck equations, or equivalently a set of coupled Langevin equations driven by white noises, is analyzed, and applications to the non-white noise problem and Kramers equation are discussed.

Keywords

Colored Noise Irrelevant Variable Path Integral Representation Gaussian Colored Noise Short Correlation Time 
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References

  1. 1.
    H. Haken, Rev.Mod.Rhys. 47, 67 (1975).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Among others: C. W. Gardiner, Phys.Rev. A89,2814 and 2823 (1984);MathSciNetADSGoogle Scholar
  3. 2a.
    W. Theiss and U. M. Titulauer; Physica 130A,183 and 143 (1985);ADSGoogle Scholar
  4. 2b.
    N. G. Van Kampen and I. Oppenheim; Physica 138A, 231 (1986).ADSGoogle Scholar
  5. 3.
    N.G.Van Kampen; Phys.Rep. 124, 69 (1985). In this review there is an extense list of references to resent papers on adiabatic elimination procedures.MathSciNetADSCrossRefGoogle Scholar
  6. 4.
    L. E. Reichel and W. C. Scieve (Eds.), “Instabilities, Bifurcations and Fluctuations in Chemical Systems (Univ. Texas Press, Austin, 1982);Google Scholar
  7. 4a.
    K. Kitahara, H. Metiu and J. Ross, J.Chem.Phys. 64, 292(1976)ADSCrossRefGoogle Scholar
  8. 4b.
    K. Kitahara, H. Metiu and J. Ross, J.Chem.Phys. 65, 393(1976);ADSCrossRefGoogle Scholar
  9. 4c.
    H. A. Weidenmul1er, Prog. Partic, and Nucl. Phys. 3, 49 (1980).ADSCrossRefGoogle Scholar
  10. 5.
    R. P. Feynman and A. R. Hibbs, “Quantum Mechanics and Path Integrals” (McGraw Hill. New York, 1965)MATHGoogle Scholar
  11. 5a.
    R. P. Feynman and F. L. Vernon, Ann.Phys. (N.Y.) 24, 118(1963).MathSciNetADSCrossRefGoogle Scholar
  12. 6.
    L. Pesquera, M. Rodriguez and E. Santos, Phys.Lett. 94A, 287 (1983)MathSciNetADSGoogle Scholar
  13. 6a.
    L. Pesquera, M. Rodriguez and E. Santos R.Phytian, J.Phys. A10, 777(1977).ADSGoogle Scholar
  14. 7.
    R. Graham, Z.Phys. B26, 281 (1977).ADSGoogle Scholar
  15. 8.
    F. Langouche, D. Roekaerts and E. Tirapegui, “Functional Integration and Semiclassical Expansions” (D.Reidel Pub. Co., Dordrecht, 1982).CrossRefMATHGoogle Scholar
  16. 9.
    D. M. Brink, Prog. Partic, and Nucl. Phys. 4, 323 (1980)ADSCrossRefGoogle Scholar
  17. 9a.
    K. Moehring and U. Smilansky, Nucl.Phys. A338, 227 (1980).ADSGoogle Scholar
  18. 10.
    N.G.Van Kampen, “Stochastic Processes in Physics and Chemistry”(North Holland, Amsterdam, 1981)MATHGoogle Scholar
  19. 10a.
    C. W. Gardiner Handbook of Stochastic Methods”(Springer-Verlag, Berlin, 1983).CrossRefMATHGoogle Scholar
  20. 11.
    J. Nordholm and P. Zwanzig, J. Stat. Phys. 13, 347 (1975)MathSciNetADSCrossRefGoogle Scholar
  21. 11a.
    H. Risken, “The Fokker-Planck Equation” (Springer-Verlag, Berlin, 1983).Google Scholar
  22. 12.
    H.S.Wio, C.Budde and C.Briozzo, to be submitted for publication.Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Horacio S. Wio
    • 1
  1. 1.Departament de Fisica, Facultat de CiencesUniversitat de les Illes BalearsPalma de MallorcaSpain

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