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Time‐Scale Invariance in Transport and Relaxation

JAN 01, 1991
Important, and often puzzling, features of transport and relaxation in disordered systems can be attributed to the long‐tailed distributions of the times between events that limit the motion.
Harvey Scher
Michael F. Shlesinger
John T. Bendler

An early theme in probability was calculating the fair ante for various games of chance. Nicolas Bernoulli introduced a seemingly innocent game, first published in 1713, that yielded a paradoxical result. The result has become known as the St. Petersburg paradox, because of an analysis written later by Daniel Bernoulli in the Commentary of the St. Petersburg Academy.

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References

  1. 1. I. Todhunter, A History of the Mathematical Theory of Probability, Cambridge U.P., Cambridge, England (1865).

  2. 2. E. W. Montroll, G. H. Weiss, J. Math. Phys. 6, 167 (1965).https://doi.org/JMAPAQ

  3. 3. E. W. Montroll, H. Scher, J. Stat. Phys. 9, 101 (1973). https://doi.org/JSTPBS
    M. F. Shlesinger, J. Stat. Phys. 10, 421 (1974). https://doi.org/JSTPBS
    H. Scher, E. W. Montroll, Phys. Rev. B 12, 2455 (1975).https://doi.org/PLRBAQ

  4. 4. M. E. Scharfe, Phys. Rev. B 2, 5025 (1970). https://doi.org/PLRBAQ
    G. Pfister, Phys. Rev. Lett. 33, 1474 (1974).https://doi.org/PRLTAO

  5. 5. H. Scher, in Proc. Seventh Int. Conf. on Amorphous and Liquid Semiconductors, Edinburgh, unpublished (1977), p. 209.
    G. Pfister, H. Scher, Adv. Phys. 27, 747 (1978).https://doi.org/ADPHAH

  6. 6. T. Tiedje, in Semiconductors and Semimetals, vol. 21C, J. Pankove, ed., Academic, New York (1984), p. 207.

  7. 7. F. C. Bos, D. M. Burland, Phys. Rev. Lett. 58, 152 (1987).https://doi.org/PRLTAO

  8. 8. H. E. BoeschJr, F. B. McLean, J. M. McGarrity, P. S. Winokur, IEEE Trans. Nucl. Sci. 25, 1239 (1978). https://doi.org/IETNAE
    F. B. McLean, H. E. Boesch Jr, T. R. Oldham, in Ionizing Radiation Effects in MOS Devices and Circuits, T. P. Ma, P. V. Dressendorfer, eds., Wiley, New York (1989), p. 87.

  9. 9. F. W. Schmidlin, Phys. Rev. B 16, 2362 (1977). https://doi.org/PLRBAQ
    J. Noolandi, Phys. Rev. B 16, 4466 (1977). https://doi.org/PLRBAQ
    A. I. Rudenko, V. I. Arkhipov, Philos. Mag. 39, 465 (1979). https://doi.org/PMAADG
    T. Tiedje, A. Rose, Solid State Commun. 37, 49 (1981). https://doi.org/SSCOA4
    J. Orenstein, M. Kastner, V. Vaninov, Philos. Mag. B 46, 23 (1982).https://doi.org/PMABDJ

  10. 10. E. Muller‐Horsche, D. Haarer, H. Scher, Phys. Rev. 35, 1273 (1987).

  11. 11. M. F. Shlesinger, Annu. Rev. Phys. Chem. 39, 269 (1988).https://doi.org/ARPLAP

  12. 12. M. Abkowitz, M. J. Rice, M. Stolka, Philos. Mag. B 61, 25 (1990).https://doi.org/PMABDJ

  13. 13. R. Cole, Annu. Rev. Phys. Chem. 40, 1 (1989). https://doi.org/ARPLAP
    G. Williams, D. C. Watts, Trans. Faraday Soc. 66, 80 (1970).https://doi.org/TFSOA4

  14. 14. A. Plonka, Time‐Dependent Reactivity of Species in Condensed Matter, Lecture Notes in Chemistry 40, Springer‐Verlag, New York (1986).

  15. 15. J. Kakalios, R. A. Street, W. B. Jackson, Phys. Rev. Lett. 59, 1037 (1987); https://doi.org/PRLTAO
    J. Kakalios, R. A. Street, W. B. Jackson, Philos. Mag. B 56, 305 (1987). https://doi.org/PMABDJ
    J. Kakalios, Hopping and Related Phenomena, World Scientific, Singapore (1990).

  16. 16. F. Kohlrausch, Pogg. Ann. Phys. 119, 352 (1863).

  17. 17. “Physics Through the 1990s,” Natl. Acad. Sci. P., Washington, D.C. (1986).

  18. 18. M. H. Cohen, G. S. Grest, Adv. Chem. Phys. 48, 455 (1981). https://doi.org/ADCPAA
    R. G. Palmer, D. Stein, E. S. Abrahams, P. W. Anderson, Phys. Rev. Lett. 53, 958 (1984).https://doi.org/PRLTAO

  19. 19. J. Klafter, M. F. Shlesinger, Proc. Natl. Acad. Sci. USA 83, 848 (1986).https://doi.org/PNASA6

  20. 20. S. Glarum, J. Chem. Phys. 33, 1371 (1960).https://doi.org/JCPSA6

  21. 21. K. L. Li, P. T. Inglefield, A. A. Jones, J. T. Bendler, A. D. English, Macromolecules 21, 2940 (1988).https://doi.org/MAMOBX

  22. 22. J. T. Bendler, Ann. N. Y. Acad. Sci. 371, 299 (1981). https://doi.org/ANYAA9
    A. A. Jones, J. F. O’Gara, P. T. Inglefield, J. T. Bendler, A. F. Yee, K. L. Ngai, Macromolecules 16, 658 (1983).https://doi.org/MAMOBX

  23. 23. R. Zallen, The Physics of Amorphous Solids, Wiley, New York (1983), chaps. 4–6.

More about the Authors

Harvey Scher. BP Research, Cleveland, Ohio.

Michael F. Shlesinger. Naval Research, Arlington, Virginia.

John T. Bendler. General Electric Company, Schenectady, New York.

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This Content Appeared In
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Volume 44, Number 1

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