Skip to main content

Applications of Path Integrals to Problems in Dissipation

  • Chapter
Book cover Path Integrals

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 34))

Abstract

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.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. P. Feynman, Ph.D. Thesis, Princeton University (1942), unpublished.

    Google Scholar 

  2. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).

    Article  MathSciNet  ADS  Google Scholar 

  3. R. P. Feynman, Phys. Rev. 84, 108 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. R. P. Feynman, F. L. Vernon, Jr., Ann. Phys. (N.Y.) 24, 118 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  5. R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals, New York: McGraw-Hill (1965).

    MATH  Google Scholar 

  6. R. P. Feynman, Statistical Mechanics, Reading, Mass.: W. A. Benjamin (1972).

    Google Scholar 

  7. R. P. Feynman, Phys. Rev. 97, 660 (1955).

    Article  ADS  MATH  Google Scholar 

  8. R. P. Feynman, R. W. Hellwarth, C. K. Iddings, P. M. Platzman, Phys. Rev. 127, 1004 (1962). FHIP.

    Article  ADS  MATH  Google Scholar 

  9. P. M. Platzman, Phys. Rev. 125, 1961 (1962).

    Article  ADS  MATH  Google Scholar 

  10. R. W. Hellwarth, P. M. Platzman, Phys. Rev. 128, 1599 (1962).

    Article  ADS  Google Scholar 

  11. P. M. Platzman, in Polarons and Excitons, C. G. Kuper, G. D. Whitfield, eds., New York: Plenum, 1963.

    Google Scholar 

  12. K. K. Thornber, Ph.D. Thesis, Part II, California Institute of Technology (1966), unpublished.

    Google Scholar 

  13. K. K. Thornber, R. P. Feynman, Phys. Rev. B1, 4099 (1970),

    Article  ADS  Google Scholar 

  14. K. K. Thornber, R. P. Feynman, Phys. Rev. B4, 674E (1971).

    Article  ADS  Google Scholar 

  15. K. K. Thornber, Phys. Rev. B3, 1929 (1971),

    Article  ADS  Google Scholar 

  16. K. K. Thornber, Phys. Rev. B4, 675E (1971).

    Article  ADS  Google Scholar 

  17. K. K. Thornber, in Polarons in Ionic Crystals and Polar Semiconductors, J. T. Devreese, ed., Amsterdam: North-Holland (1972).

    Google Scholar 

  18. K. K. Thornber, Phys. Rev. B9, 3489 (1974).

    Article  ADS  Google Scholar 

  19. 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. J. T. Devreese, J. deSitter, M. Goovarts, Phys. Rev. B5, 2367 (1972).

    Article  ADS  Google Scholar 

  21. L. F. Lemmens, J. T. Devreese, Solid-State Commun. 12, 1067 (1973).

    Article  ADS  Google Scholar 

  22. L. F. Lemmens, J. de Sitter, J. T. Devreese, Phys. Rev. B8, 2717 (1973).

    Article  ADS  Google Scholar 

  23. H. B. Callen, T. A. Welton, Phys. Rev. 83, 34 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. K. K. Thornber, in preparation.

    Google Scholar 

  25. R. Courant, D. Hilbert, Methods of Mathematical Physics II, New York: Interscience (1962) Ch. 2.

    MATH  Google Scholar 

  26. J. T. Devreese, R. Evrard, in Ref. 17.

    Google Scholar 

  27. L. van Hove, Physica 21, 517 (1955).

    Article  MathSciNet  MATH  Google Scholar 

  28. L. van Hove, Physica 23, 441 (1957).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. W. Kohn, J. M. Luttinger, Phys. Rev. 108, 590 (1957).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Price, IBM J. Research and Devel. 10, 395 (1966).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer Science+Business Media New York

About this chapter

Cite this chapter

Thornber, K.K. (1978). Applications of Path Integrals to Problems in Dissipation. In: Papadopoulos, G.J., Devreese, J.T. (eds) Path Integrals. NATO Advanced Study Institutes Series, vol 34. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-9140-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-9140-1_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-9142-5

  • Online ISBN: 978-1-4684-9140-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics