The Uses of Path Integrals for Diffusion in Bistable Potentials

  • U. Weiss
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 11)


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].


Optical Bistability Tunnel Diode Autocatalytic Chemical Reaction Bistable System Saddle Point Method 
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  1. 1.
    H.A. Kramers, Physica 7: 284 (1940)CrossRefGoogle Scholar
  2. 2.
    R. Landauer and J.A. Swanson, Phys. Rev. 121: 1668 (1961); R.Landauer, J.Phys.Soc.Japan 41: 695 (1976)Google Scholar
  3. 3.
    R. Landauer and J.W.F. Woo, in “Synergetics”, H.Haken, ed. ( Teubner, Stuttgart 1973 )Google Scholar
  4. 4.
    H. Haken, Synergetics, An Introduction, 2nd ed., Springer Series in Synergetics, Vol. 1 ( Springer Berlin, Heidelberg, New York 1978 )Google Scholar
  5. 5.
    R. Bonifacio et al., IEEE Journal of Quantum Electronics, QE-17: 357(1981) and references thereinCrossRefGoogle Scholar
  6. 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. 7.
    W. Weidlich, “Progress in Synergetics” (Erice Summer School, 1974 ), H. Haken, ed. ( North-Holland, Amsterdam, 1974 )Google Scholar
  8. 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 )CrossRefGoogle Scholar
  9. 9.
    F. Haake, Phys.Rev.Lett. 41: 1685 (1978); F. de Pasquale and P.Tombesi, Phys.Lett. 72A: 45 (1979)CrossRefGoogle Scholar
  10. 10.
    B. Caroli, C. Caroli and B. Roulet, J.Stat.Phys. 21: 415 (1979)CrossRefGoogle Scholar
  11. 11.
    U. Weiss and W. Haeffner, in “Functional Integration”, ed. by J.P. Antoine and E. Tirapegui ( Plenum, New York, 1980 )Google Scholar
  12. 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)CrossRefGoogle Scholar
  13. 13.
    B. Caroli, C. Caroli and B. Roulet, “Diffusion in a Bistable Potential: The Functional Integral Approach”, preprint 1980Google Scholar
  14. 14.
    J.L. Gervais and B. Sakita, Phys.Rev. D11: 2943 (1975)Google Scholar
  15. 15.
    A.M. Polyakov, Nucl. Phys. B121: 429 (1977); E. Gildener and A. Patrascioiu, Phys. Rev. D16: 423 (1977)CrossRefGoogle Scholar
  16. 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. 17.
    J.H. van Vleck, Proc. Natl. Acad. Sci. 14: 178(1928); F.Langouche, D. Roekaerts and E. Tirapegui, Physi ca97A: 195(1979)PubMedCrossRefGoogle Scholar
  18. 18.
    U. Weiss, to be publishedGoogle Scholar
  19. 19.
    M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, ( Dover Publications, New York, 1965 )Google Scholar
  20. 20.
    R.F. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D10, 4114 (1974)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • U. Weiss
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgartFed. Rep. of Germany

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