Journal of Statistical Physics

, Volume 19, Issue 4, pp 333–340 | Cite as

Generalized master equations under delocalized initial conditions

  • V. M. Kenkre


The initial condition term that must be appended to the generalized master equation (GME) when the density matrix is not initially diagonal in the representation chosen is studied and explicit expressions are obtained for several cases. The term is shown to vanish for initial occupation of a Bloch state of arbitrary wave vector if the system is a crystal and the representation is that of site states, despite the violation of the initial diagonality condition. It is pointed out how one is to use the expressions for the initial term in transport calculations.

Key words

Generalized master equations initial diagonality localized and delocalized conditions exciton transport in molecular crystals 


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  1. 1.
    N. van Kampen,Adv. Chem. Phys. 15:65 (1965).Google Scholar
  2. 2.
    E. W. Montroll, inEnergetics in Metallurgical Phenomena (Gordon and Breach, New York, 1967), Vol. 3, p. 123.Google Scholar
  3. 3.
    I. Oppenheim, K. E. Shuler, and G. Weiss,Stochastic Processes in Chemical Physics: The Master Equation (MIT Press, Cambridge, Mass., 1977).Google Scholar
  4. 4.
    L. van Hove,Physica 23:441 (1957).Google Scholar
  5. 5.
    A. Janner, L. van Hove, and E. Verboven,Physica 28:1341 (1962).Google Scholar
  6. 6.
    I. Prigogine and P. Résibois,Physica 27:629 (1961).Google Scholar
  7. 7.
    S. Nakajima,Prog. Theor. Phys. 20:948 (1958).Google Scholar
  8. 8.
    R. Zwanzig, inLectures in Theoretical Physics, W. Downs and J. Downs, eds. (Boulder, Colorado, 1961), Vol. III.Google Scholar
  9. 9.
    E. W. Montroll, inFundamental Problems in Statistical Mechanics Vol. I, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1962).Google Scholar
  10. 10.
    R. Swenson,J. Math. Phys. 3:1017 (1962).Google Scholar
  11. 11.
    G. G. Emch,Helv. Phys. Acta 37:532 (1964).Google Scholar
  12. 12.
    V. M. Kenkre, inStatistical Mechanics and Statistical Methods in Theory and Application, U. Landman, ed. (Plenum Press, 1977).Google Scholar
  13. 13.
    V. M. Kenkre and R. S. Knox,Phys. Rev. B 9:5279 (1974);J. Luminescence 12:187 (1976), and references therein.Google Scholar
  14. 14.
    C. Aslangul and Ph. Kottis,Phys. Rev. B 13:5544 (1976).Google Scholar
  15. 15.
    V. M. Kenkre,Phys. Rev. B 11:3406 (1975).Google Scholar
  16. 16.
    V. M. Kenkre,Phys. Lett. 63A:367 (1977);Phys. Rev. B (October 1978).Google Scholar
  17. 17.
    P. Avakian, V. Ern, R. Merrifield, and A. Suna,Phys. Rev. 165:974 (1968).Google Scholar
  18. 18.
    H. Haken and P. Reineker,Z. Physik 249:253 (1972).Google Scholar
  19. 19.
    M. Grover and R. Silbey,J. Chem. Phys. 54:4843 (1971).Google Scholar
  20. 20.
    R. Hemenger, K. Lakatos-Lindenberg, and R. Pearlstein,J. Chem. Phys. 60:3271 (1974).Google Scholar
  21. 21.
    V. M. Kenkre,Phys. Lett. 65A:391 (1978).Google Scholar
  22. 22.
    E. W. Montroll,J. Math. Phys. 10:753 (1969).Google Scholar
  23. 23.
    R. S. Knox, inTopics in Photosynthesis, Vol. 11, J. Barber, ed. (Elsevier, 1977).Google Scholar
  24. 24.
    M. Fayer and C. B. Harris,Phys. Rev. B 9:748 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • V. M. Kenkre
    • 1
  1. 1.Institute for Fundamental Studies and Department of Physics and AstronomyUniversity of RochesterRochester

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