Advertisement

Physik der kondensierten Materie

, Volume 13, Issue 2, pp 89–100 | Cite as

A relation of response functions and correlation functions to the random walk problem inμ-space for uniform systems in nonequilibrium transport theory

  • W. A. Schlup
Article

Abstract

The Boltzmann equation for a uniform system of nondegenerate electrons in a constant field containing an additive, normconserving perturbation termg k is solved by comparison with the Green’s function solution of the unperturbed equation. Linear response coefficients can be expressed by the conditional probability as a linear functional ing k .

Keywords

Random Walk Conditional Probability Boltzmann Equation Function Solution Transport Theory 
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.

Zusammenfassung

Die Boltzmanngleichung eines homogenen Systems nicht entarteter Elektronen in einem konstanten Feld mit einem additiven, normerhaltenden Störtermg k wird durch Vergleichen mit der Greenfunktion des ungestörten Problems gelöst. Lineare Responsekoeffizienten können mittels der bedingten Wahrscheinlichkeit als lineares Funktional ing k ausgedrückt werden.

Résumé

L’équation de Boltzmann contenant un terme de perturbation additiveg k , qui conserve la norme est résolue pour un système homogène d’électrons non dégénerés dans un champ constant. La solution s’obtient par comparaison avec la fonction de Green de l’équation non-perturbée. Les coéfficients de résponse linéaire sont exprimables comme fonctionelles linéaires eng k à l’aide de la probabilité conditionelle.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Price, P. J.: IBM J. Res. Developm.1, 147 (1957).MathSciNetGoogle Scholar
  2. 2.
    ——: IBM J. Res. Developm.1, 239 (1957).MathSciNetCrossRefGoogle Scholar
  3. 3.
    ——: IBM J. Res. Developm.2, 200 (1958).Google Scholar
  4. 4.
    ——: J. Phys. Chem. Solids8, 136 (1959).CrossRefADSGoogle Scholar
  5. 5.
    ——: IBM J. Res. Developm.3, 191 (1959).Google Scholar
  6. 6.
    ——: Fluctuation Phenomena in Solids, R. E. Burgess (ed.), Chapt. 8. New York and London: Academic Press 1965.Google Scholar
  7. 7.
    Gurevich, V. L.: Soviet Physics-JETP16, 1252 (1963).ADSGoogle Scholar
  8. 7a.
    ——, Katilyus, R.: Soviet Physics-JETP22, 796 (1966).ADSGoogle Scholar
  9. 8.
    Lax, M.: Rev. mod. Phys.32, 25 (1960).CrossRefADSMATHGoogle Scholar
  10. 9.
    Schlup, W. A.: Phys. kondens. Materie8, 167 (1968).ADSGoogle Scholar
  11. 10.
    Gantsevich, S. V., Gurevich, V. L., Katilyus, R.: Soviet Physics Solid State11, 247 (1969).Google Scholar
  12. 11.
    Bakshi, P. M., Gross, E. P.: Ann. Phys. (N.Y.)49, 513 (1968).CrossRefADSGoogle Scholar
  13. 12.
    Schlup, W. A.: Phys. kondens. Materie10, 116 (1969).ADSGoogle Scholar
  14. 13.
    Vliet, K. M. van, Fassett, J. R.: Fluctuation Phenomena in Solids. R. E. Burgess (ed.), Chapt. 7. New York and London: Academic Press 1965.Google Scholar
  15. 14.
    Landau, L. D., Lifshitz, E. M.: Lehrbuch der theoretischen Physik, vol. V, p. 392. Berlin: Academic Verlag 1966.Google Scholar
  16. 15.
    Kubo, R.: Rep. progr. Phys.29, pt. I, 255 (1966), (Institute of Physics and Physical Society, London 1966).CrossRefADSMATHGoogle Scholar
  17. 16.
    Martin, P. C.: Many-body Physics, de Witt (ed.). Gordon Breach, New York: Bollon 1967, p. 66.Google Scholar
  18. 17.
    Doob, J. L.: Stochastic Processes. London: John Wiley 1953, p. 509.MATHGoogle Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • W. A. Schlup
    • 1
  1. 1.IBM Zurich Research LaboratoryRüschlikonSwitzerland

Personalised recommendations