Path Integrals pp 359-382 | Cite as

Applications of Path Integrals to Problems in Dissipation

  • K. K. Thornber
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 34)


Feynman’s path-integral method offers a unique approach to problems involving the transport of electrons in dissipative media in electric and magnetic fields. This is because actual, physical dissipative systems can be approximated by similar dissipative systems which can be solved exactly using path integrals. The difference between the exact and approximate systems can then be treated as a perturbation. Several examples are considered including both a.c.-linear and d.c.-nonlinear response as well as the problem of electron acceleration in sub-threshold fields. The latter problem appears to require a more detailed understanding of the scattering in the presence of the field than do transport problems.


Boltzmann Equation Path Integral Dissipative System Cross Term General Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. P. Feynman, Ph.D. Thesis, Princeton University (1942), unpublished.Google Scholar
  2. 2.
    R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    R. P. Feynman, Phys. Rev. 84, 108 (1951).MathSciNetADSCrossRefzbMATHGoogle Scholar
  4. 4.
    R. P. Feynman, F. L. Vernon, Jr., Ann. Phys. (N.Y.) 24, 118 (1963).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals, New York: McGraw-Hill (1965).zbMATHGoogle Scholar
  6. 6.
    R. P. Feynman, Statistical Mechanics, Reading, Mass.: W. A. Benjamin (1972).Google Scholar
  7. 7.
    R. P. Feynman, Phys. Rev. 97, 660 (1955).ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    R. P. Feynman, R. W. Hellwarth, C. K. Iddings, P. M. Platzman, Phys. Rev. 127, 1004 (1962). FHIP.ADSCrossRefzbMATHGoogle Scholar
  9. 9.
    P. M. Platzman, Phys. Rev. 125, 1961 (1962).ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    R. W. Hellwarth, P. M. Platzman, Phys. Rev. 128, 1599 (1962).ADSCrossRefGoogle Scholar
  11. 11.
    P. M. Platzman, in Polarons and Excitons, C. G. Kuper, G. D. Whitfield, eds., New York: Plenum, 1963.Google Scholar
  12. 12.
    K. K. Thornber, Ph.D. Thesis, Part II, California Institute of Technology (1966), unpublished.Google Scholar
  13. 13.
    K. K. Thornber, R. P. Feynman, Phys. Rev. B1, 4099 (1970),ADSCrossRefGoogle Scholar
  14. 13a.
    K. K. Thornber, R. P. Feynman, Phys. Rev. B4, 674E (1971).ADSCrossRefGoogle Scholar
  15. 14.
    K. K. Thornber, Phys. Rev. B3, 1929 (1971),ADSCrossRefGoogle Scholar
  16. 14a.
    K. K. Thornber, Phys. Rev. B4, 675E (1971).ADSCrossRefGoogle Scholar
  17. 15.
    K. K. Thornber, in Polarons in Ionic Crystals and Polar Semiconductors, J. T. Devreese, ed., Amsterdam: North-Holland (1972).Google Scholar
  18. 16.
    K. K. Thornber, Phys. Rev. B9, 3489 (1974).ADSCrossRefGoogle Scholar
  19. 17.
    K. K. Thornber, in Linear and Nonlinear Electron Transport in Solids, J. T. Devreese, V. E. van Doren, eds., New York: Plenum (1976).Google Scholar
  20. 18.
    J. T. Devreese, J. deSitter, M. Goovarts, Phys. Rev. B5, 2367 (1972).ADSCrossRefGoogle Scholar
  21. 19.
    L. F. Lemmens, J. T. Devreese, Solid-State Commun. 12, 1067 (1973).ADSCrossRefGoogle Scholar
  22. 20.
    L. F. Lemmens, J. de Sitter, J. T. Devreese, Phys. Rev. B8, 2717 (1973).ADSCrossRefGoogle Scholar
  23. 21.
    H. B. Callen, T. A. Welton, Phys. Rev. 83, 34 (1951).MathSciNetADSCrossRefzbMATHGoogle Scholar
  24. 22.
    K. K. Thornber, in preparation.Google Scholar
  25. 23.
    R. Courant, D. Hilbert, Methods of Mathematical Physics II, New York: Interscience (1962) Ch. 2.zbMATHGoogle Scholar
  26. 24.
    J. T. Devreese, R. Evrard, in Ref. 17.Google Scholar
  27. 25.
    L. van Hove, Physica 21, 517 (1955).MathSciNetCrossRefzbMATHGoogle Scholar
  28. 26.
    L. van Hove, Physica 23, 441 (1957).MathSciNetADSCrossRefzbMATHGoogle Scholar
  29. 27.
    W. Kohn, J. M. Luttinger, Phys. Rev. 108, 590 (1957).MathSciNetADSCrossRefzbMATHGoogle Scholar
  30. 28.
    Price, IBM J. Research and Devel. 10, 395 (1966).CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • K. K. Thornber
    • 1
  1. 1.IncorporatedBell LaboratoriesMurray HillUSA

Personalised recommendations