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The Uses of Path Integrals for Diffusion in Bistable Potentials

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Chaos and Order in Nature

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 11))

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Abstract

It has become clear in recent years that bistable macrosystems play a fundamental role in many fields of physics, chemistry, biology and also sociology. Among the vast literature we mention only a few: BROWNIAN motion in a field of force [l], fluctuations in tunnel diodes [2] and cooperative phenomena in data processing [3] one-mode laser [4], optical bistability [5], autocatalytic chemical reactions[6] and interacting social groups [7].

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References

  1. H.A. Kramers, Physica 7: 284 (1940)

    Article  CAS  Google Scholar 

  2. R. Landauer and J.A. Swanson, Phys. Rev. 121: 1668 (1961); R.Landauer, J.Phys.Soc.Japan 41: 695 (1976)

    Google Scholar 

  3. R. Landauer and J.W.F. Woo, in “Synergetics”, H.Haken, ed. ( Teubner, Stuttgart 1973 )

    Google Scholar 

  4. H. Haken, Synergetics, An Introduction, 2nd ed., Springer Series in Synergetics, Vol. 1 ( Springer Berlin, Heidelberg, New York 1978 )

    Google Scholar 

  5. R. Bonifacio et al., IEEE Journal of Quantum Electronics, QE-17: 357(1981) and references therein

    Article  Google Scholar 

  6. F. Schlögl, Z. Phys. 253: 147 (1972); I.Matheson, D.F.Walls and C.W.Gardiner, J.Stat.Phys. 12: 21 (1975)

    Google Scholar 

  7. W. Weidlich, “Progress in Synergetics” (Erice Summer School, 1974 ), H. Haken, ed. ( North-Holland, Amsterdam, 1974 )

    Google Scholar 

  8. M. Suzuki, J.Stat.Phys. 16: 11 (1977); M. Suzuki, in Systems Far From Equilibrium, 1980 Sitges Int. Conf. on Statistical Mechanics, ed. by L. Garrido, Lecture Notes in Physics, Vol. 132 ( Springer Berlin, Heidelberg, New York 1980 )

    Article  Google Scholar 

  9. F. Haake, Phys.Rev.Lett. 41: 1685 (1978); F. de Pasquale and P.Tombesi, Phys.Lett. 72A: 45 (1979)

    Article  CAS  Google Scholar 

  10. B. Caroli, C. Caroli and B. Roulet, J.Stat.Phys. 21: 415 (1979)

    Article  Google Scholar 

  11. U. Weiss and W. Haeffner, in “Functional Integration”, ed. by J.P. Antoine and E. Tirapegui ( Plenum, New York, 1980 )

    Google Scholar 

  12. R.S. Larson and M.D. Kostin, J. Chem. Phys. 69: 4821 (1978); W.Weidlich and H.Grabert, Z.Phys. B36: 283 (1980); W.Bez and P.Talkner, Phys.Lett. 82A: 313 (1981)

    Article  CAS  Google Scholar 

  13. B. Caroli, C. Caroli and B. Roulet, “Diffusion in a Bistable Potential: The Functional Integral Approach”, preprint 1980

    Google Scholar 

  14. J.L. Gervais and B. Sakita, Phys.Rev. D11: 2943 (1975)

    Google Scholar 

  15. A.M. Polyakov, Nucl. Phys. B121: 429 (1977); E. Gildener and A. Patrascioiu, Phys. Rev. D16: 423 (1977)

    Article  Google Scholar 

  16. S. Coleman, “The Uses of Instantons”, Lectures delivered at the 1977 International School of Subnuclear Physics, Ettore Majorana,(Plenum, New York 1979 )

    Google Scholar 

  17. J.H. van Vleck, Proc. Natl. Acad. Sci. 14: 178(1928); F.Langouche, D. Roekaerts and E. Tirapegui, Physi ca97A: 195(1979)

    Article  PubMed  Google Scholar 

  18. U. Weiss, to be published

    Google Scholar 

  19. M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, ( Dover Publications, New York, 1965 )

    Google Scholar 

  20. R.F. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D10, 4114 (1974)

    CAS  Google Scholar 

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© 1981 Springer-Verlag Berlin Heidelberg

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Weiss, U. (1981). The Uses of Path Integrals for Diffusion in Bistable Potentials. In: Haken, H. (eds) Chaos and Order in Nature. Springer Series in Synergetics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68304-6_19

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  • DOI: https://doi.org/10.1007/978-3-642-68304-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-68306-0

  • Online ISBN: 978-3-642-68304-6

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