Skip to main content
SpringerLink
Log in

The expansion of the configurational diffusion equation in inverse powers of the frictional constant: Further progress in the calculation of coefficients by functional integral methods

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

In this paper the coefficients of the diffusion equation for a unidimensional mechanical system are calculated up toO(1/β7), in terms of the frictional constant β. This procedure is a variant of the one used previously, which is based on splitting the velocity into a deterministic plus a rapidly fluctuating part. This splitting was adjusted so as to make the memory integral, which appears in the expression for the diffusion coefficient, vanish. Consequently, the deterministic part of the velocity results to satisfy a modified Hamilton-Jacobi dissipative equation in configuration space. Here, a new expansion of the response function is introduced, so as to make calculations more expeditious.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hie-Tae Moon,Rev. Mod. Phys.,65 (1993) 1535.

    Article  ADS  Google Scholar 

  2. Coffey W. T., Evans M. W. andGrigolini P.,Molecular Diffusion and Spectra (Wiley, New York, N.Y.) 1984, p. 215.

    Google Scholar 

  3. Evans M. andRielich S. (Editors),Adv. Chem. Phys., Vol. 85 (John Wiley and Sons, New York N.Y.) 1993.

    Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Hanggi P., Marchesoni F. andGrigolini P. Z. Phys. B,56 (1984) 333.

    Article  ADS  Google Scholar 

  6. Fox R. F.,Phys. Rev. A,37 (1988) 911.

    Article  MathSciNet  ADS  Google Scholar 

  7. Perico A., Pratolongo R., Freed R. F., Pastor R. W., Szabo A.,J. Chem. Phys.,98 (1992) 564.

    Article  ADS  Google Scholar 

  8. Ferrando R., Spadacini R. andTommei G. E.,Physica A,196 (1993) 83.

    Article  ADS  Google Scholar 

  9. Yamakawa H.,Modern Theory of Polymer Solutions (Harper and Row, New York, N.Y.) 1971.

    Google Scholar 

  10. Danle P. S., Siolander A. andSingwi R. S.,Phys. Rev.,165 (1968) 277.

    Article  ADS  Google Scholar 

  11. Henery R. J.,J. Phys. A,4 (1971) 885.

    Article  Google Scholar 

  12. Onsager L. andMachlup S.,Phys. Rev.,91 (1953) 1505.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Mazur P. andBedeaux D.,Physica A,173 (1991) 155.

    Article  MathSciNet  ADS  Google Scholar 

  14. Prigogine I. andDefay R.,Chemical Thermodynamics (Longmans Green, London) 1952, Chapt. 3.

    Google Scholar 

  15. Jahnig F. andRichter P. H.,J. Chem. Phys.,64 (1976) 4645.

    Article  ADS  Google Scholar 

  16. Adelman S. A.,Adv. Chem. Phys.,44 (1980) 143.

    Article  Google Scholar 

  17. von Smoluchovski M. Ann. Phys. (N.Y.),25 (1908) 205.

    Article  ADS  Google Scholar 

  18. Einstein, A.,Ann. Phys. (N.Y.),33, (1910) 1275.

    Article  ADS  MATH  Google Scholar 

  19. Uhlenbeck G. E. andOrnstein L. S.,Phys. Rev.,36 (1930) 823.

    Article  ADS  MATH  Google Scholar 

  20. Wang M. C. andUhlenbeck G. E. Rev. Mod. Phys.,17 (1945) 323.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Battezzati M. andPerico A.,J. Chem. Phys.,74 (1981) 4527.

    Article  MathSciNet  ADS  Google Scholar 

  22. Chandrasekhar S.,Rev. Mod. Phys.,15 (1943) 1.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. van Kampen N. G.,Phys. Rep.,24 (1976) 171.

    Article  MathSciNet  ADS  Google Scholar 

  24. Hanggi P. andThomas H. Phys. Rep. C,88 (1982) 209.

    Article  MathSciNet  ADS  Google Scholar 

  25. Volkov V. S. andPokrovski V. N.,J. Math. Phys.,24 (1983) 267.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Adelman S. A. andGarrison B. J.,Mol. Phys.,33 (1977) 1671.

    Article  MathSciNet  ADS  Google Scholar 

  27. Fox R. F.,J. Math. Phys.,18 (1977) 2331.

    Article  ADS  MATH  Google Scholar 

  28. de Groot S. R. andMazur P.,Nonequilibrium Thermodynamics (North-Holland, Amsterdam) 1961, Chapt. 9.

    Google Scholar 

  29. Battezzati M.,Chem. Phys. Lett. 164 (1989) 363.

    Article  MathSciNet  ADS  Google Scholar 

  30. Callen H. B. andWelton T. A.,Phys. Rev.,83 (1951) 34.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Epstein B.,Partial Differential Equations (Mc Graw-Hill, New York, N.Y.) 1962, Chapt. 2.

    MATH  Google Scholar 

  32. Battezzati M.,Nuovo Cimento B,50 (1979) 7.

    Article  MathSciNet  ADS  Google Scholar 

  33. Battezzati M.,Chem. Phys. Lett.,167 (1990) 137.

    Article  ADS  Google Scholar 

  34. Battezzati M.,Phys. Lett. A,179 (1992) 119.

    Article  ADS  Google Scholar 

  35. Battezzati M.,Chem. Phys. Lett.,216 (1993) 585.

    Article  ADS  Google Scholar 

  36. San Miguel M. andSancho M.,J. Stat. Phys.,22 (1980) 605.

    Article  MathSciNet  ADS  Google Scholar 

  37. Dekker H.,Phys. Lett. A,90 (1982) 26.

    Article  MathSciNet  ADS  Google Scholar 

  38. Fox R. F.,Phys. Rev. A,33 (1986) 467.

    Article  MathSciNet  ADS  Google Scholar 

  39. Venkatesh T. G. andPotnaik L. M.,Phys. Rev. E,38 (1993) 2402.

    Article  ADS  Google Scholar 

  40. Landau L. andLifshitz E.,Théorie quantique relativiste (Mir, Moscow) 1972, Chapt. 8.

    Google Scholar 

  41. Fox R. F.,Phys. Rev. A,41 (1990) 2969.

    Article  MathSciNet  ADS  Google Scholar 

  42. Battezzati M.,Nuovo Cimento B,70 (1982) 13.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Istituto di Cibernetica e Biofisica del CNR, 16146, Genova, Italy

    M. Battezzati

Authors
  1. M. Battezzati
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Battezzati, M. The expansion of the configurational diffusion equation in inverse powers of the frictional constant: Further progress in the calculation of coefficients by functional integral methods. Nuov Cim B 110, 1287–1306 (1995). https://doi.org/10.1007/BF02723113

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02723113

PACS

PACS

Search

Navigation