Stochastic Electrodynamics: Methods and Results

  • Pierre Claverie
Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)


Stochastic Electrodynamics (SED) is a classical theory of particles and fields. The difference with respect to usual Electrodynamics is the assumption of a universal stochastic electromagnetic field (“background” field or “zero-point” field), which could be conceived as a classical counterpart to the vacuum field of Quantum Electrodynamics (QED). Thus this stochastic field (uniform and isotropic) has zero mean and spectral density [1–4].


Anharmonic osciLLator KepLer Problem Stochastic Force Detailed Balance Condition Stochastic Field 


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  1. [1]
    P. CLAVERIE and S. DINER, Intern. J. Quant. Chem. 12, Suppl. 1, 41 (1977)Google Scholar
  2. [2]
    E. SANTOS, Nuovo Cimento (série 111 19B, 57 (1974).Google Scholar
  3. [3]
    T.H. BOYER, Phys. Rev. D11, 790 (1975).ADSGoogle Scholar
  4. [4]
    T.W. MARSHALL, Proc. Roy. Soc. (London) A276, 475 (1963).ADSCrossRefMATHGoogle Scholar
  5. [5]
    L. De La PENA-AUERBACH and A.M. CETTO, Rev. Mex. Fis. 25, 1 (1976).Google Scholar
  6. [6]
    L. De La PENA-AUERBACH and A.M. CETTO, J. Math. Phys. 18, 1612 (1977).ADSCrossRefGoogle Scholar
  7. [7]
    P. CLAVERIE and S. DINER, p. 395 in “Localization and Delocalization in Quantum Chemistry”, ed. by 0. Chalvet, R. Daudel, S. Diner and J.P. Malrieu ( Reidel, Dordrecht, 1976 ).CrossRefGoogle Scholar
  8. [8]
    Ming Chen WANG and G.E. UHLENBECK, Rev. Mod. Phys. 17, 323 (1945). Reprinted in “Selected Papers on Noise and Stochastic Processes”, ed. by N. Wax ( Dover, New York, 1954 ).Google Scholar
  9. [9]
    L. De La PENA and A.M. CETTO, J. Math. Phys. 20, 469 (1979).ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    M. LAX, Rev. Mod. Phys. 38, 541 (1966).ADSCrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    R.L. STRATONOVICH, chap. 1, in “Conditional Markov Processes and their Application to the Theory of Optimal Control” (American Elsevier, New York, 1968 ) (Russian original: Moscow University Press, Moscow, 1966 ).Google Scholar
  12. [12]
    R.Z. KHAS’MINSKII, Theory Prob. Appl. 11, 390 (1966).CrossRefGoogle Scholar
  13. [13]
    G.C. PAPANICOLAOU and J.B. KELLER, SIAM J. Appl. Math. 21, 287 (1971).CrossRefMathSciNetGoogle Scholar
  14. [14]
    G.C. PAPANICOLAOU and R. HERSH, Indiana Univ. Math. J. 21, 815 (1972).MATHMathSciNetGoogle Scholar
  15. [15]
    R. COGBURN and R. HERSH, Indiana Univ. Math. J. 22, 1067 (1973).MATHMathSciNetGoogle Scholar
  16. [16]
    ]G.C. PAPANICOLAOU, p.209 in “Modern Modelling of Continuum Phenomena”, Lectures in Applied Mathematics, vol. 16, Ed. by R.C. Di Prima ( American Mathematical Society, Providence, Rhode Island, 1977 ).Google Scholar
  17. [17]
    R. KUBO, J. Math. Phys. 4, 174 (1963).ADSCrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    A. BRISSAUD and U. FRISCH, J. Math. Phys. 15, 524 (1974).ADSCrossRefMATHMathSciNetGoogle Scholar
  19. [19]
    N.G. VAN KAMPEN, Phys. Repts. (Phys. Letters C) 24C, 171 (1976).Google Scholar
  20. [20]
    R. ZWANZIG (a) J. Chem. Phys. 33, 1338 (1964); (b) Physica, 30, 1109 (1964).MathSciNetGoogle Scholar
  21. [21]
    U. FRISCH (a) Ann. Astrophys. 29, 645 (1966) and 30, 565 (1967) (b) p. 75 in “Probabilistic Methods in Applied Mathematics”, ed. by A.T. Bharucha-Reid ( Academic Press, New York, 1968 ).Google Scholar
  22. [22]
    R.H. TERWIEL, Physica, 74, 248 (1974).ADSCrossRefMathSciNetGoogle Scholar
  23. [23]
    N.G. VAN KAMPEN, Physica 74, 215 and 239 (1974).Google Scholar
  24. [24]
    M.M. TROPPER, J. Stat. Phys. 17, 491 (1977).ADSCrossRefMATHMathSciNetGoogle Scholar
  25. [25]
    P. HÄNGGI, Zeitschr. Phys. B31, 407 (1978).Google Scholar
  26. [26]
    P. CLAVERIE and S. DINER “Some Remarks about the LAX Approximation in Stochastic Electrodynamics”. Technical Report (1977).Google Scholar
  27. [27]
    T.W. MARSHALL, “Brownian motion and quasi-Markov processes”, parts I and II (submitted to PhysicalGoogle Scholar
  28. [28]
    T.W. MARSHALL and P. CLAVERIE, Brownian motion and quasi-Markov processes, part III (submitted to Physica).Google Scholar
  29. [29]
    H. HAKEN, Rev. Mod. Phys. 47, 67 (1975). (See especially section XI.C.2.).Google Scholar
  30. [30]
    T.W. MARSHALL and P. CLAVERIE “Stochastic Electrodynamics of nonlinear system. I. Particle in a central field of force” J. Math. Phys. (in press).Google Scholar
  31. [31]
    P. CLAVERIE, L. De La PENA-AUERBACH and S. DINER, “Stochastic Electrodynamics of non-Linear systems. II. Derivation of a reduced Fokker-Planck equation in terms of relevant constants of motion” (to be published).Google Scholar
  32. [32]
    R. KUBO, J. Phys. Soc. Japan, 12, 570 (1957).CrossRefGoogle Scholar
  33. [33]
    H. GOLDSTEIN, “Classical Mechanics”, Addison-Wesley, Reading, Massachusetts (1956).chap. 9, section 9. 7.Google Scholar
  34. [34]
    H.C. CORBEN and P. STEHLE, “Classical Mechanics”, 2nd edition, Wiley, New York (1960).chap. 11, section 64.Google Scholar
  35. [35]
    L. PESQUERA and P. CLAVERIE, “Derivation of Fokker-Planck equations through response theory”, to be published.Google Scholar
  36. [36]
    P. JULG, (a) Folia Chimica Theoretica Latina, 6, 99 (1978); (b) Results to be published.Google Scholar
  37. [37] a)
    L. PESQUERA, “The anharmonic oscillator in Stochastic Electro-dynamics (SED): the problem of “radiation balance” at each frequency”, communication in these. Proceed’nss •Google Scholar
  38. b).
    L. PESQUERA and P. CLAVERIE, “The quartic anharmonic oscillator in Stochastic Electrodynamics, to be published.Google Scholar
  39. [38]
    G.N. WATSON, “A Treatise on the Theory of Bessel Functions”, Cambridge University Press (1966).Google Scholar
  40. [39]
    T.W. MARSHALL, “On the sum of a family of Kapteyn series” (submitted to Z.A.M.P. (J. Appl. Math. Phys.)).Google Scholar
  41. [40]
    L. PESQUERA, P. CLAVERIE and A. DENIS, “Stochastic Electrodynamics of non-linear systems. III. Accurate stationary solution for the hydrogen.atom” (to be published).Google Scholar

Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • Pierre Claverie
    • 1
  1. 1.Institut de Biologie Physico-ChimiqueLaboratoire de Chimie Quantique (Université de Paris VI)ParisFrance

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