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Manifolds of equivalent path integral solutions of the Fokker-Planck equation

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Zeitschrift für Physik B Condensed Matter

Abstract

Path integral solutions of the multi-dimensional Fokker-Planck equation with variable dependent diffusion coefficients are deduced in a simple and exact manner. We show that the Onsager-Machlup function is not defined uniquely but is definable only together with the discretization prescription and the measure in the functional space. We present wide classes of mathematical equivalent path integral representations characterized by nonlinear variable transformationsv(q′, q) and the coefficientsα K of a linear combination, all giving exactly the same solution of the Fokker-Planck equation.

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References

  1. Stratonovich, R.L.: Topics in the Theory of Random Noise, Vol. 1, New York: Gordon and Breach 1963

    Google Scholar 

  2. Kubo, R., Matsuo, K., Kitahara, K.: J. Stat. Phys.9, 51 (1973)

    Google Scholar 

  3. Graham, R.: Springer Tracts in Modern Physics, Vol. 66, New York (1973)

  4. Graham, R. In: Fluctuations, Instabilities and Phase Transitions, Riste (ed.) New York: Plenum 1976

    Google Scholar 

  5. Horsthemke, W., Bach, A.: Z. Physik B22, 189 (1975)

    Google Scholar 

  6. Janssen, H.-K.: Z. Physik B23, 377 (1976)

    Google Scholar 

  7. Haken, H.: Z. Physik B24, 321 (1976)

    Google Scholar 

  8. Graham, R.: Phys. Rev. Lett.38, 51 (1977)

    Google Scholar 

  9. Bach, A., Dürr, D., Stawicki, B.: Z. Physik B26, 191 (1977)

    Google Scholar 

  10. Graham, R.: Z. Physik B26, 281 (1977)

    Google Scholar 

  11. Leschke, H., Schmutz, M.: Z. Physik B27, 85 (1977)

    Google Scholar 

  12. Onsager, L., Machlup, S.: Phys. Rev.91, 1505, 1512 (1953)

    Google Scholar 

  13. Kerler, W., preprint 1978

  14. Smirnov, W.I.: Lehrgang der Höheren Mathematik, Vol. I, Berlin 1967

  15. Graham, R. In: Stochastic Processes in Nonequilibrium Systems, Proceedings, Sitges 1978, Lecture Notes in Physics, Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  16. Gel'fand, I.M., Yaglom, A.M.: J. Math. Phys.1, 48 (1960)

    Google Scholar 

  17. Graham, R. In: Statphys.13, Proceedings, Haifa 1977

Download references

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Authors and Affiliations

  1. Fachbereich Physik, Philipps-Universität Marburg, Rentof 6, D-3550, Marburg/Lahn, Germany

    C. Wissel

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  1. C. Wissel
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Wissel, C. Manifolds of equivalent path integral solutions of the Fokker-Planck equation. Z Physik B 35, 185–191 (1979). https://doi.org/10.1007/BF01321245

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  • DOI: https://doi.org/10.1007/BF01321245

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