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Motion in a double-well potential with additive colored Gaussian noise

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Zeitschrift für Physik B Condensed Matter

Abstract

The overdamped motion of particles in the double-well potential−ax 2/2+bx 4/4 with additive exponentially correlated noise is investigated. By solving an appropriate two-variable Fokker-Planck equation in terms of matrix continued fractions, stationary distribution functions in one and two variables as well as eigenvalues and correlation functions are obtained.

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References

  1. Kramers, H.A.: Physica7, 284 (1940)

    Google Scholar 

  2. Landauer, R., Swanson, A.: Phys. Rev.121, 1668 (1961)

    Google Scholar 

  3. Landauer, R.: J. Appl. Phys.33, 2209 (1962)

    Google Scholar 

  4. Dykman, M.I., Krivoglaz, M.A.: Synergetics, Proceedings of the International Symposium, Tallinn 1983, p. 33

  5. Hänggi, P.: Phys. Lett.78A, 304 (1980)

    Google Scholar 

  6. Chandler, D.: J. Chem. Phys.68, 2959 (1978)

    Google Scholar 

  7. Berne, B.J., Skinner, J.L., Wolynes, P.G.: J. Chem. Phys.73, 4314 (1980)

    Google Scholar 

  8. Hasha, D.L., Eguchi, T., Jonas, J.: J. Chem. Phys.73, 1571 (1981); J. Am. Chem. Soc.104, 2290 (1982)

    Google Scholar 

  9. Garrity, D.K., Skinner, J.L.: Chem. Phys. Lett.95, 46 (1983)

    Google Scholar 

  10. Carmeli, B., Nitzan, A.: J. Chem. Phys. Lett.80, 3596 (1984)

    Google Scholar 

  11. Staab, H.A.: Einführung in die Theoretische Organische Chemie 4. Auflage, 2. Nachdruck. Weinheim: Verlag Chemie, 1970

    Google Scholar 

  12. Brinkman, H.C.: Physica22, 29 (1956); Physica22, 149 (1956)

    Google Scholar 

  13. Blomberg, C.: Physica86A, 49 (1977)

    Google Scholar 

  14. Visscher, P.B.: Phys. Rev. B14, 347 (1976)

    Google Scholar 

  15. Skinner, J.L., Wolynes, P.G.: J. Chem. Phys.69, 4821 (1978)(a); J. Chem. Phys.72, 1392 (1980)(b)

    Google Scholar 

  16. Larson, R.S., Kostin, M.D.: J. Chem. Phys.69, 4821 (1978)(a); J. Chem. Phys.72, 1392 (1980)(b)

    Google Scholar 

  17. Northrup, S.C., Hynes, J.T.: J. Chem. Phys.69, 5246 (1978); J. Chem. Phys.69, 5261 (1978); J. Chem. Phys.73, 2700 (1980)

    Google Scholar 

  18. Mangel, M.: J. Chem. Phys.72, 6606 (1980)

    Google Scholar 

  19. Schulten, K., Schulten, Z., Szabo, A.: J. Chem. Phys.74, 4426 (1981)

    Google Scholar 

  20. Krumhansl, J.A., Schriefer, J.R.: Phys. Rev. B11, 3535 (1975)

    Google Scholar 

  21. Landau, L.D., Lifschitz, E.M.: Lehrbuch der Theoretischen Physik. Band V (Statistische Physik). Berlin: Academie Verlag (1975)

    Google Scholar 

  22. Hänggi, P.: J. Stat. Phys.30, 401 (1983)

    Google Scholar 

  23. Voigtlaender, K., Risken, H.: J. Stat. Phys.40, 397 (1985)

    Google Scholar 

  24. Schenzle, A., Graham, R.: Phys. Lett.98A 319 (1983)

    Google Scholar 

  25. Schenzle, A.: Habilitationsschrift, Gesamthochschule Essen (1984)

  26. Dixit, S.N., Zoller, P., Lambropulos, P.: Phys. Rev. A21, 1289 (1980)

    Google Scholar 

  27. Zoller, P., Alber, G., Salvador, R.: Phys. Rev. A24, 398 (1981)

    Google Scholar 

  28. Sancho, J.M., San Miguel, M., Katz, S.L., Gunton, J.D.: Phys. Rev. A26, 1589 (1982)

    Google Scholar 

  29. Sancho, J.M., San Miguel, M., Jamazaki, H., Kawakubo, T.: Physica116A, 560 (1982)

    Google Scholar 

  30. Hernandez-Machado, A., San Miguel, M., Sancho, J.M.: Phys. Rev. A29, 3388 (1984)

    Google Scholar 

  31. Hernandez-Machado, A., San Miguel, M.: “Stochastic methods applied to physics” Singapore: World Scientific Publications 1985 (to appear)

  32. Hernandez-Machado, A., San Miguel, M., Katz, S.L.: Phys. Rev. A31, (1985)

  33. Hernandez-Machado, A., San Miguel, M.: J. Math. Phys.25 1066 (1984)

    Google Scholar 

  34. Hänggi, P., Marchesoni, F., Grigolini, P.: Z. Phys. B — Condensed Matter56, 333 (1984)

    Google Scholar 

  35. Hänggi, P., Mroczkowski, T.J., Moss, F., McClintock, P.V.E.: Phys. Rev. A (rapid communications)32, 695 (1985)

    Google Scholar 

  36. Hänggi, P., Riseborough, P.: Phys. Rev. A27, 3379 (1983)

    Google Scholar 

  37. Hänggi, P., Mojtabai, F.: Phys. Rev. A26, 1168 (1982)

    Google Scholar 

  38. Carmeli, B., Nitzan, A.: Phys. Rev. Lett.49, 423 (1982)

    Google Scholar 

  39. Carmeli, B., Nitzan, A.: Phys. Lett.102A, 517 (1983)

    Google Scholar 

  40. Horsthemke, W., Lefever, R.: Noise induced transitions. In: Springer Series in Synergetics. Vol. 15. Heidelberg, Berlin, New York: Springer 1984

    Google Scholar 

  41. Marchesoni, F., Grigolini, P.: J. Chem. Phys.78, 6297 (1983)

    Google Scholar 

  42. Grigolini, P.: J. Stat. Phys.27, 283 (1982)

    Google Scholar 

  43. Grote, R., Hynes, J.T.: J. Chem. Phys.73, 2715 (1980)

    Google Scholar 

  44. Risken, H., Vollmer, H.D.: Z. Phys. B — Condensed Matter33, 297 (1979)

    Google Scholar 

  45. Vollmer, H.D., Risken, H.: Z. Phys. B — Condensed Matter34, 313 (1979)

    Google Scholar 

  46. Risken, H.: The Fokker-Planck equation. In: Springer Series in Synergetics Vol. 18. Berlin: Springer (1984)

    Google Scholar 

  47. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. New York: Dover Publications, Inc. (1972)

    Google Scholar 

  48. Jung, P., Risken, H.: Z. Phys. B — Condensed Matter54, 357 (1984)

    Google Scholar 

  49. Jung, P., Risken, H.: Z. Phys. B — Condensed Matter59, 469 (1985)

    Google Scholar 

  50. Moss, F., McClintock, P.V.E.: Z. Phys. B — Condensed Matter61, 381 (1985)

    Google Scholar 

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Authors and Affiliations

  1. Abteilung für Theoretische Physik, Universität Ulm, Oberer Eselsberg, D-7000, Ulm, Germany

    P. Jung & H. Risken

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  1. P. Jung
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  2. H. Risken
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Jung, P., Risken, H. Motion in a double-well potential with additive colored Gaussian noise. Z. Physik B - Condensed Matter 61, 367–379 (1985). https://doi.org/10.1007/BF01317805

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  • DOI: https://doi.org/10.1007/BF01317805

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