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Quantum and stochastic aspects of low-temperature trapping and reaction dynamics

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Abstract

We discuss theoretical work on motion-limited trapping kinetics at very low temperatures where theories based upon strictly diffusive models break down due to quantum mechanical effects. In addition, we present numerical results which confirm earlier asymptotic predictions regarding the survival probability for one-dimensional chains, and discuss the important role fluctuations and selfaveraging (or the lack thereof) play in the analysis of finite systems.

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References

  1. H. C. Wolf, inAdvances in Atomic and Molecular Physics, Vol. 3, D. R. Bates and I. Estermann, eds. (Academic Press, New York, 1976); R. C. Powell and Z. Soos,J. Lumin. 11:1 (1975).

    Google Scholar 

  2. H. Auweter, A. Braun, U. Mayer, and D. Schmid,Z. Naturforsch. 34A:761 (1979); H. Auweter, U. Mayer, and D. Schmid,Z. Naturforsch. 33A:651 (1978).

    Google Scholar 

  3. A. Braun, U. Mayer, H. Auweter, H. C. Wolf, and D. Schmid,Z. Naturforsch. 37A:1013 (1982).

    Google Scholar 

  4. A. H. Francis and R. Kopelman, inExcitation Dynamics in Molecular Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981).

    Google Scholar 

  5. R. Kopelman, inSpectroscopy and Excitation Dynamics of Condensed Molecular Systems, V. M. Agranovich and R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983).

    Google Scholar 

  6. R. Kopelman,J. Stat. Phys. 42:185 (1986).

    Google Scholar 

  7. D. D. Dlott, M. D. Fayer, and R. D. Wieting,J. Chem. Phys. 67:3808 (1977).

    Google Scholar 

  8. D. D. Dlott, M. D. Fayer, and R. D. Wieting,J. Chem. Phys. 69:2752 (1978).

    Google Scholar 

  9. R. A. Auerbach and G. L. McPherson,Phys. Rev. B 33:6815 (1986).

    Google Scholar 

  10. J. R. G. Thorne, R. G. Denning, T. J. Barker, and D. I. Grimley,J. Phys. (Paris)C7:125 (1985).

    Google Scholar 

  11. J. Cibert, M. C. Terrile, and Y. Merle d'Aubigne,J. Phys. (Paris)C7:135 (1985).

    Google Scholar 

  12. U. Even, K. Rademann, J. Jortner, N. Manor, and R. Reisfeld,Phys. Rev. Lett. 58:285 (1987);42:2164 (1984).

    Google Scholar 

  13. W. D. Dozier, J. M. Drake, and J. Klafter,Phys. Rev. Lett. 56:197 (1986).

    Google Scholar 

  14. T. Kirski, J. Grimm, and C. von Borczyskowski,J. Chem. Phys. 87:2062 (1987).

    Google Scholar 

  15. E. W. Montroll,Proc. Symp. Appl. Math. Am. Soc. 16:193 (1964); E. W. Montroll and G. H. Weiss,J. Math. Phys. 6:167 (1965).

    Google Scholar 

  16. G. H. Weiss,Proc. Natl. Acad. Sci. USA 77:4391 (1980); G. H. Weiss and R. J. Rubin,Adv. Chem. Phys. 52:363 (1983).

    Google Scholar 

  17. H. B. Rosenstock,Phys. Rev. 187:1166 (1969);J. Math. Phys. 21:1643 (1980).

    Google Scholar 

  18. S. Smoluchowski,Ann. Phys. (Leipzig)48:1103 (1915).

    Google Scholar 

  19. G. Zumofen and A. Blumen,Chem. Phys. Lett. 88:63 (1982); A. Blumen and G. Zumofen,Chem. Phys. Lett. 70:387 (1980).

    Google Scholar 

  20. J. Klafter, G. Zumofen, and A. Blumen,J. Phys. Lett. (Paris)45:L49 (1984).

    Google Scholar 

  21. J. Klafter and R. Silbey,J. Chem. Phys. 72:849 (1979);74:3510 (1981).

    Google Scholar 

  22. S. Havlin, B. Trus, G. H. Weiss, and D. J. Ben-Avraham,J. Phys. A 18:L247 (1985); S. Havlin, M. Dishon, J. E. Kiefer, and G. H. Weiss,Phys. Rev. Lett. 53:407 (1984).

    Google Scholar 

  23. D. L. Huber, inExcitation Dynamics in Molecular Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981);Phys. Rev. B 20:2307, 5333 (1979).

    Google Scholar 

  24. D. L. Huber,Phys. Rev. B 20:2307 (1979).

    Google Scholar 

  25. D. L. Huber,Phys. Rev. B 20:5333 (1979).

    Google Scholar 

  26. D. L. Huber,J. Chem. Phys. 75:4749 (1981); K. K. Gosh and D. L. Huber,Phys. Rev. B 23:4441 (1981).

    Google Scholar 

  27. K. Lakatos-Lindenberg, R. P. Hemenger, and R. M. Pearlstein,J. Chem. Phys. 56:4852 (1972).

    Google Scholar 

  28. V. M. Kenkre and Y. M. Wong,Phys. Rev. B 22:5716 (1980);23:3748 (1981).

    Google Scholar 

  29. V. M. Kenkre and P. E. Parris,Phys. Rev. B 27:3221 (1983).

    Google Scholar 

  30. V. M. Kenkre, inExciton Dynamics in Molecular Crystals and Aggregates, K. G. Hohler, ed. (Springer, Berlin, 1982).

    Google Scholar 

  31. V. M. Kenkre, P. E. Parris, and D. Schmid,Phys. Rev. B 32:4946 (1985).

    Google Scholar 

  32. P. E. Parris and V. M. Kenkre,Chem. Phys. Lett. 107:413 (1984); P. E. Parris and V. M. Kenkre,J. Lumin. 31:612 (1984).

    Google Scholar 

  33. B. Movaghar,J. Phys. C: Solid State 13:4915 (1980); B. Movaghar, G. W. Sauer, and D. Wurtz,J. Stat. Phys. 27:473 (1982).

    Google Scholar 

  34. H. Scher and C. H. Wu,Proc. Natl. Acad. Sci. USA 78:22 (1980);J. Chem. Phys. 74:5366 (1981).

    Google Scholar 

  35. R. Grassberger and I. Procaccia,J. Chem. Phys. 77:6281 (1981).

    Google Scholar 

  36. J. Anlauf,Phys. Rev. Lett. 52:1845 (1984).

    Google Scholar 

  37. F. Kayser and J. B. Hubbard,Phys. Rev. Lett. 51:79 (1983).

    Google Scholar 

  38. P. E. Parris,Phys. Lett. A 114:250 (1986); P. E. Parris, V. M. Kenkre, and S. M. Phatak,J. Stat. Phys. 35:749 (1986); V.M. Kenkre, P. E. Parris, and S. M. Phatak,Physica 128A:571 (1984).

    Google Scholar 

  39. T. Lubensky,Phys. Rev. A 30:1845 (1984).

    Google Scholar 

  40. B. Ya. Balagurov and V. G. Vaks,Zh. Eksp. Teor. Fiz. 65:1939 (1973) [Sov. Phys. JETP 38:968 (1974)].

    Google Scholar 

  41. M. D. Donsker and S. R. S. Varadhan,Commun. Pure Appl. Math. 28:525 (1975).

    Google Scholar 

  42. M. Bramson and J. L. Lebowitz,Phys. Rev. Lett. 61:2397 (1988).

    Google Scholar 

  43. Th. M. Nieuwenhuizen,Phys. Rev. Lett. 62:357 (1989).

    Google Scholar 

  44. K. Lakatos-Lindenberg, R. P. Hemenger, and R. M. Pearlstein,J. Chem. Phys. 56:4852 (1972); R. P. Hemenger, K. Lakatos-Lindenberg, and R. M. Pearlstein,J. Chem. Phys. 60:3271 (1974); R. M. Pearlstein,J. Chem. Phys. 56:4852 (1972); R. P. Hemenger and R. M. Pearlstein,Chem. Phys. 2:424 (1973).

    Google Scholar 

  45. V. M. Kenkre,Phys. Status Solidi B 89:651 (1978).

    Google Scholar 

  46. D. L. Huber,Phys. Rev. B 22:1714 (1980);24:1083 (1981).

    Google Scholar 

  47. P. E. Parris,Phys. Rev. Lett. 62:1392 (1989).

    Google Scholar 

  48. P. E. Parris,Phys. Rev. B 40:4928 (1989).

    Google Scholar 

  49. J. W. Edwards and P. E. Parris,Phys. Rev. B 40:8045 (1989);J. Lumin. 45:279 (1990).

    Google Scholar 

  50. H. Benk and R. Silbey,J. Chem. Phys. 79:3487 (1983).

    Google Scholar 

  51. U. Seiferheld, H. Bassler, and B. Movaghar,Phys. Rev. Lett. 51:813 (1983); I. G. Hunt, D. Bloor, and B. Movaghar,J. Phys. C 18:3497 (1985).

    Google Scholar 

  52. I. M. Lifshitz,Adv. Phys. 13:483 (1964).

    Google Scholar 

  53. J. Luttinger and R. Tao,Ann. Phys. (N.Y.)145:185 (1983); R. Freidberg and J. M. Luttinger,Phys. Rev. B 12:4460 (1975).

    Google Scholar 

  54. R. J. Elliot, J. A. Krumhansl, and P. L. Leath,Rev. Mod. Phys. 46:465 (1974).

    Google Scholar 

  55. E. N. Economou,Green's Functions in Quantum Physics (Springer-Verlag, New York, 1979).

    Google Scholar 

  56. A. J. Van Strien, J. F. C. van Kooten, and J. Schmidt,Chem. Phys. Lett. 76:7 (1980); A. J. Van Strien, J. Schmidt, and R. Silbey,Mol. Phys. 46:151 (1982).

    Google Scholar 

  57. J. W. Haus and K. W. Kehr,Phys. Rep. 150:265 (1987).

    Google Scholar 

  58. P. E. Parris, unpublished results.

  59. D. L. Huber and W. Y. Ching, presented at the 7th Conference on Dynamical Processes in Excited States of Solids, Athens, Georgia (August 1989), and unpublished results.

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  1. University of Missouri-Rolla, 65401, Rolla, Missouri

    P. E. Parris

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Parris, P.E. Quantum and stochastic aspects of low-temperature trapping and reaction dynamics. J Stat Phys 65, 1161–1172 (1991). https://doi.org/10.1007/BF01049605

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