Advertisement

Continuous Stochastic Models

Chapter
Part of the Topics in Current Physics book series (TCPHY, volume 15)

Abstract

This chapter concentrates on continuous models for the dynamics of superionic conductors as opposed to jump models and lattice gas models, which are considered in Chap.4. By continuous models we mean that the diffusion of an ion is not represented by instantaneous jumps from an equilibrium site to another one, but by a continuous motion in between.

Keywords

Langevin Equation Random Force Superionic Conductor Diffusive Motion Jump Diffusion 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 8.1
    W.H. Flygare, R.A. Huggins: J. Phys. Chem. Solids 34, 1199 (1973).ADSCrossRefGoogle Scholar
  2. 8.2
    J.B. Boyce, T.M. Hayes, W. Stutius, J.C. Mikkelsen, Jr.: Phys. Rev. Lett. 38, 1362 (1977).ADSCrossRefGoogle Scholar
  3. 8.3
    G. Eckold, K. Funke, J. Kalus, R.E. Lechner: J. Phys. Chem. Solids 37, 1097 (1976).ADSCrossRefGoogle Scholar
  4. 8.4
    R.J. Cava, F. Reidinger, B.J. Wuensch: Solid State Commun. 24, 411 (1977).ADSCrossRefGoogle Scholar
  5. 8.5
    P. Vashishta, A. Rahman: Phys. Rev. Lett. 40, 1337 (1978).ADSCrossRefGoogle Scholar
  6. 8.6
    W. Bührer, P. Brüesch: Solid State Commun. 16, 155 (1975).CrossRefGoogle Scholar
  7. 8.7
    G.L. Bottger, C.V. Damsgard: J. Chem. Phys. 57, 1215 (1972).ADSCrossRefGoogle Scholar
  8. 8.8
    O.B. Ajayi, L.E. Nagel, I.D. Raistrick, R.A. Huggins: J. Phys. Chem. Solids 37, 167 (1976).ADSCrossRefGoogle Scholar
  9. 8.9
    W.G. Kleppmann, H. Bilz: Commun. Phys. 1, 105 (1976).Google Scholar
  10. 8.10
    W.G. Kleppmann: J. Phys. C. 9, 2285 (1976).ADSCrossRefGoogle Scholar
  11. 8.11
    M.J. Rice, W.L. Roth: J. Solid State Chem. 4, 294 (1972).ADSCrossRefGoogle Scholar
  12. 8.12
    C.W. Haas: J. Solid State Chem. 7, 155 (1973).ADSCrossRefGoogle Scholar
  13. 8.13
    G. Eckold, K. Funke, J. Kalus, R.E. Lechner: Phys. Lett. 55 A, 125 (1975).ADSGoogle Scholar
  14. 8.14
    H. Sato, R. Kikuchi: J. Chem. Phys. 55, 677 (1971).ADSCrossRefGoogle Scholar
  15. 8.15
    R. Kikuchi, H. Sato: J. Chem. Phys. 55, 702 (1971).ADSCrossRefGoogle Scholar
  16. 8.16
    F.G. Mahan, W.J. Pardee: Phys. Lett. 49 A, 325 (1974).ADSGoogle Scholar
  17. 8.17
    W.J. Pardee, G.D. Mahan: J. Solid State Chem. 15, 310 (1975).ADSCrossRefGoogle Scholar
  18. 8.18
    H. Hinkelmann, B.A. Huberman: Solid State Commun. 19, 365 (1976).ADSCrossRefGoogle Scholar
  19. 8.19
    H. Hinkelmann: Solid State Commun. 21, 975 (1977).ADSCrossRefGoogle Scholar
  20. 8.20
    R. Vargas, M.B. Salamon, C.P. Flynn: Phys. Rev.Lett. 37, 1550 (1976).ADSCrossRefGoogle Scholar
  21. 8.21
    G.D. Mahan: Phys. Rev. B 14, 780 (1976).ADSCrossRefGoogle Scholar
  22. 8.22
    P.M. Richards: Phys. Rev. B 16, 1393 (1977).MathSciNetADSCrossRefGoogle Scholar
  23. 8.23
    W. Bührer, W. Hälg: Helv. Phys. Acta 47, 27 (1974).Google Scholar
  24. 8.24
    A.F. Wright, B.E.F. Fender: J. Phys. C 10, 2261 (1977).ADSCrossRefGoogle Scholar
  25. 8.25
    S. Hoshino, T. Sakuma, Y. Fujii: Solid State Commun. 22, 763 (1977).ADSCrossRefGoogle Scholar
  26. 8.26
    S. Hoshino: J. Phys. Soc. Jpn. 12, 315 (1957).ADSCrossRefGoogle Scholar
  27. 8.27
    G. Burley: J. Phys. Chem. Solids 25, 629 (1964).ADSCrossRefGoogle Scholar
  28. 8.28
    K.R. Subbaswamy, G.D. Mahan: Phys. Rev. Lett. 37, 642 (1976).ADSCrossRefGoogle Scholar
  29. 8.29
    F. Claro, G.D. Mahan: J. Phys. C 10, L73 (1977).ADSCrossRefGoogle Scholar
  30. 8.30
    M. Girvin, G.D. Mahan: Solid State Commun. 23, 629 (1977).ADSCrossRefGoogle Scholar
  31. 8.31
    F.L. Lederman, M.B. Salamon, H. Peisl: Solid State Commun. 19, 147 (1976).ADSCrossRefGoogle Scholar
  32. 8.32
    M.B. Salamon: Phys. Rev. B 15, 2236 (1977).ADSCrossRefGoogle Scholar
  33. 8.33
    H.U. Beyeler, L. Pietronero, S. Strässler, H.J. Wiesmann: Phys. Rev. Lett. 38, 1532 (1977).ADSCrossRefGoogle Scholar
  34. 8.34
    L. Lam, A. Bunde: Z. Phys. 30, 65 (1978).Google Scholar
  35. 8.35
    B.A. Huberman: Phys. Rev. Lett. 32, 1000 (1974).ADSCrossRefGoogle Scholar
  36. 8.36
    M.J. Rice, S. Strässler, G.A. Toombs: Phys. Rev. Lett. 32, 596 (1974).ADSCrossRefGoogle Scholar
  37. 8.37
    B.A. Huberman, P.N. Sen: Phys. Rev. Lett. 33, 1379 (1974).ADSCrossRefGoogle Scholar
  38. 8.38
    P. Brüesch, S. Strässler, H.R. Zeller: Phys. Status Solidi (a) 31, 217 (1975).ADSCrossRefGoogle Scholar
  39. 8.39
    P. Fulde, L. Pietronero, W.R. Schneider, S. Strässler: Phys. Rev. Lett. 35, 1776 (1975).ADSCrossRefGoogle Scholar
  40. 8.40
    B.A. Huberman, R.M. Martin: Phys. Rev. B 13, 1498 (1976).ADSCrossRefGoogle Scholar
  41. 8.41
    K.R. Subbaswamy: Solid State Commun. 19, 1157 (1976).ADSCrossRefGoogle Scholar
  42. 8.42
    K.R. Subbaswamy: Solid State Commun. 21, 371 (1977).ADSCrossRefGoogle Scholar
  43. 8.43
    G.H. Wannier: Statistical Physios (Wiley and Sons, New York 1966).Google Scholar
  44. 8.44
    R. Kubo: J. Phys. Soc. Jpn. 12, 570 (1957).MathSciNetADSCrossRefGoogle Scholar
  45. R. Kubo: Rep. Progr. Phys. 29, 255 (1966).ADSCrossRefGoogle Scholar
  46. 8.45
    e.g. T. Springer: Quasielastic Neutron Scattering for the Investigation of diffusive Motions in Solids and Liquids, Springer Tracts in Modern Physics, Vol. 64 (Springer, Berlin, Heidelberg, New York 1972).Google Scholar
  47. 8.46
    M. Balkanski (ed.): Lattice Dynamics, International Conference Paris 1977 (Flammarion, Paris 1978).Google Scholar
  48. 8.46a
    T. Geisel: In Ref.8.46, p.549.Google Scholar
  49. 8.47
    P.A. Egelstaff, P. Schofield: Nucl. Sci. Eng. 12, 260 (1962).Google Scholar
  50. 8.48
    K.S. Singwi, A. Sjölander: Phys. Rev. 119, 863 (1960).ADSCrossRefGoogle Scholar
  51. 8.49
    V.S. Oskotskii: Sov. Phys.-Solid State 5, 789 (1963).Google Scholar
  52. 8.50
    C.T. Chudley, R.J. Elliott: Proc. Phys. Soc. (London) 77, 353 (1961).ADSCrossRefGoogle Scholar
  53. 8.51
    V.F. Sears: Proc. Phys. Soc. (London) 86, 953 (1965).ADSCrossRefGoogle Scholar
  54. 8.52
    Y. Nakahara, H. Takahashi: Proc. Phys. Soc. (London) 89, 749 (1966).ADSCrossRefGoogle Scholar
  55. 8.53
    P.S. Damle, A. Sjölander, K.S. Singwi: Phys. Rev. 165, 277 (1968).ADSCrossRefGoogle Scholar
  56. 8.54
    Caroli, G. Jannink, D. Saint-James: J. Phys. C 4, 545 (1971).ADSCrossRefGoogle Scholar
  57. 8.55
    G. Wyllie: J. Phys. C 4, 564 (1971).ADSCrossRefGoogle Scholar
  58. 8.56
    R. Kubo: Rep. Progr. Phys. 29, 255 (1966).ADSCrossRefGoogle Scholar
  59. 8.57
    e.g. H. Haken: Synergetics, an Introduction, 2nd ed. (Springer, Berlin, Heidelberg, New York 1978) p.86.zbMATHGoogle Scholar
  60. 8.58
    For an elementary introduction see F. Reif: Fundamentals of statistical and thermal physics (McGraw-Hill, New York 1965) Chap.15.11.Google Scholar
  61. 8.59
    R.L. Stratonovich: Topics in the Theory of Random Noise, Vol.1 (Gordon and Breach, New York 1963).Google Scholar
  62. 8.60
    H. Haken: Rev. Mod. Phys. 47, 67 (1975).MathSciNetADSCrossRefGoogle Scholar
  63. 8.61
    A.T. Bharucha-Reid: Elements of the Theory of Markov Processes and Their Applications (McGraw-Hill, New York 1960) Chap.3.zbMATHGoogle Scholar
  64. 8.62
    W.R. Schneider, S. Strässler: Z. Phys. B 27, 357 (1977).ADSCrossRefGoogle Scholar
  65. 8.63
    W. Dieterich, I. Peschel, W.R. Schneider: Z. Phys. B 27, 177 (1977).ADSCrossRefGoogle Scholar
  66. 8.64
    T. Geisel: Solid State Commun. 24, 155 (1977).ADSCrossRefGoogle Scholar
  67. 8.65
    W. Dieterich, T. Geisel, I. Peschel: Z. Phys. B 29, 5 (1978).ADSCrossRefGoogle Scholar
  68. 8.66
    H. Risken, H.D. Vollmer: Preprint (1978), submitted to Z. Phys..Google Scholar
  69. 8.67
    H. Mori: Progr. Theor. Phys. 33, 423 (1965).ADSzbMATHCrossRefGoogle Scholar
  70. 8.68
    H. Mori: Progr. Theor. Phys. 34, 399 (1965).ADSCrossRefGoogle Scholar
  71. 8.69
    W.R. Schneider: Z. Phys. B 24, 135 (1976).MathSciNetADSCrossRefGoogle Scholar
  72. 8.70
    H.S. Wall: Analytic Theory of Continued Fractions (Chelsa, New York 1948) P.197.zbMATHGoogle Scholar
  73. 8.71
    H.A. Kramers: Physica 7, 284 (1940).MathSciNetADSzbMATHCrossRefGoogle Scholar
  74. 8.72
    C.A. Wert: Phys. Rev. 79, 601 (1950).ADSCrossRefGoogle Scholar
  75. 8.73
    Y.M. Ivanchenko, L.A. Zil’berman: Sov. Phys.-JETP 28, 1272 (1969).ADSGoogle Scholar
  76. 8.74
    V. Ambegaokar, B.I. Halperin: Phys. Rev. Lett. 22, 1364 (1969).ADSCrossRefGoogle Scholar
  77. 8.75
    H.R. Zeller, P. Brüesch, L. Pietronero, S. Strässler: In Superionic Conductors, ed. by G.D. Mahan, W.L. Roth (Plenum Press, New York 1976) p.201.Google Scholar
  78. 8.76
    P. Brüesch, L. Pietronero, H.R. Zeller: J. Phys. C 9, 3977 (1976).ADSCrossRefGoogle Scholar
  79. 8.77
    P. Brüesch, L. Pietronero, S. Strässler, H.R. Zeller: Electrochim. Acta 22, 717 (1977).CrossRefGoogle Scholar
  80. 8.78
    P. Brüesch, L. Pietronero, S. Strässler, H.R. Zeller: Phys. Rev. B 15, 4631 (1977).ADSCrossRefGoogle Scholar
  81. 8.79
    W. Jost, K. Funke, A. Jost: Z. Naturforsch. 25a, 983 (1970).ADSGoogle Scholar
  82. 8.80
    U. Strom, P.C. Taylor, S.G. Bishop, T.L. Reinecke, K.L. Ngai: Phys. Rev. B 13, 3329 (1976).ADSCrossRefGoogle Scholar
  83. 8.81
    G. Eckold, K. Funke: Z. Naturforsch. 28a, 1042 (1973).ADSGoogle Scholar
  84. 8.82
    S.J. Allen, Jr., A.S. Cooper, F. DeRosa, J.P. Remeika, S.K. Ulasi: Phys. Rev. B 17, 4031 (1978).ADSCrossRefGoogle Scholar
  85. 8.83
    See e.g., C. Kittel: Introduction to Solid State Physics, 4th ed. (Wiley and Sons, New York 1971) p.181.Google Scholar
  86. 8.84
    P.N. Sen, B.A. Huberman: Phys. Rev. Lett. 34, 1059 (1975).ADSCrossRefGoogle Scholar
  87. 8.85
    A. Rahman, K.S. Singwi, A. Sjölander: Phys. Rev. 126, 997 (1962).ADSzbMATHCrossRefGoogle Scholar
  88. 8.86
    S.J. Allen, Jr., J.P. Remeika: Phys. Rev. Lett. 33, 1478 (1974).ADSCrossRefGoogle Scholar
  89. 8.87
    See e.g., M.V. Klein: In Light Scattering in Solids, ed. by M. Balkanski, R.C.C. Leite, S.P.S. Porto (Flammarion, Paris 1976) p.351.Google Scholar
  90. 8.88
    G. Winterling, W. Senn, M. Grimsditch, R. Katiyar: In Ref.8.46, p.553.Google Scholar
  91. 8.89
    P.M. Morse, H. Feshbach: Methods of Theoretical Physics (McGraw-Hill, New York 1953) p.884.zbMATHGoogle Scholar
  92. 8.90
    S.M. Shapiro, D. Semmingsen, M.B. Salamon: In Ref.8.46, p.538.Google Scholar
  93. 8.91
    B. Dorner, J. Windscheif, W. von der Osten: In Ref.8.46, p.535.Google Scholar
  94. 8.92
    R.C. Hanson, T.A. Fjeldly, H.D. Hochheimer: Phys. Status Solidi (b) 70, 567 (1975).ADSCrossRefGoogle Scholar
  95. 8.93
    G. Burns, F.H. Dacol, M.W. Shafer: Solid State Commun. 19, 291 (1976).ADSCrossRefGoogle Scholar
  96. 8.94
    M.J. Delaney, S. Ushioda: Solid State Commun. 19, 297 (1976).ADSCrossRefGoogle Scholar
  97. 8.95
    M.J. Delaney, S. Ushioda: Phys. Rev. B 16, 1410 (1977).ADSCrossRefGoogle Scholar
  98. 8.96
    R. Alben, G. Burns: Phys. Rev. B 16, 3746 (1977).ADSCrossRefGoogle Scholar
  99. 8.97
    CH. Hao, L.L. Chase, G.D. Mahan: Phys. Rev. B 13, 4306 (1976).ADSCrossRefGoogle Scholar
  100. 8.98
    L.G. Chase: In Ref.8.75, p.299.Google Scholar
  101. 8.99
    D. Gallagher, M.V. Klein: J. Phys. C 9, L687 (1976).ADSCrossRefGoogle Scholar
  102. 8.100
    R.A. Field, D.A. Gallagher, M.V. Klein: Preprint 1978, submitted to Phys. Rev. B.Google Scholar
  103. 8.101
    R.J. Elliott, W. Hayes, W.G. Kleppmann, A.J. Rushworth, J.F. Ryan: Proc. R. Soc. (London) A 360, 317 (1978).ADSCrossRefGoogle Scholar
  104. 8.102
    e.g. B.J. Berne, R. Pecora: Dynamic Light Scattering (Wiley and Sons, New York 1976).Google Scholar
  105. 8.103
    B.A. Huberman, R.M. Martin: Phys. Rev. Lett. 39, 478 (1977).ADSCrossRefGoogle Scholar
  106. 8.104
    D. Forster: Eydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, New York 1975).Google Scholar
  107. 8.105
    R. Zeyher: In Ref.8.46, p.532.Google Scholar
  108. 8.106
    K.W. Becker: Unpublished.Google Scholar
  109. 8.107
    H. Mori, H. Fujisaka: Progr. Theor. Phys. 49, 764 (1973).ADSCrossRefGoogle Scholar
  110. 8.108
    H. Mori, H. Fujisaka, H. Shigematsu: Progr. Theor. Phys. 51, 109 (1974).ADSCrossRefGoogle Scholar
  111. 8.109
    A. Rahman: J. Chem. Phys. 65, 4845 (1976).ADSCrossRefGoogle Scholar
  112. 8.110
    G. Jacucci, A. Rahman: Preprint 1978.Google Scholar
  113. 8.111
    Y.S. Kim, R.G. Gordon: J. Chem. Phys. 60, 4332 (1974).ADSCrossRefGoogle Scholar
  114. 8.112
    W. Schommers: Phys. Rev. Lett. 38, 1536 (1977).ADSCrossRefGoogle Scholar
  115. 8.113
    W. Schommers: Phys. Rev. B 17, 2057 (1978).ADSCrossRefGoogle Scholar
  116. 8.114
    M. Remoissenet: Solid State Commun. 27, 681 (1978).ADSCrossRefGoogle Scholar
  117. 8.115
    A.R. Bishop: J. Phys. C 11, L329 (1978).ADSCrossRefGoogle Scholar
  118. 8.116
    L. Pietronero, S. Strässler: Solid State Commun. 27, 1041 (1978).ADSCrossRefGoogle Scholar
  119. 8.117
    A.R. Bishop, T. Schneider (eds.): Solitons and Condensed Matter Physics, Springer Series in Solid-State Sciences, Vol.8 (Springer, Berlin, Heidelberg, New York 1978)Google Scholar
  120. 8.118
    W. Dieterich, I. Peschel: To be published.Google Scholar
  121. 8.119
    T. Geisel: To be published.Google Scholar
  122. A.K. Das, P. Schwendiman: Fokker-Planck equation for a periodic potential. Physica 89A, 605 (1977).ADSGoogle Scholar
  123. R. Festa, E.G. d’Agliano: Diffusion coefficient for a Brownian particle in a periodic field of force. Physica 90A, 229 (1978).ADSGoogle Scholar
  124. R.A. Field, D.A. Gallagher, M.V. Klein: Rayleigh-Brillouin spectra of the solid electrolyte RbAg4I5. Phys. Rev. B 18, 2995 (1978).ADSCrossRefGoogle Scholar
  125. J. Jäckie: Long-wavelength density fluctuations in superionic conductors. Z. Phys. B 30, 255 (1978).CrossRefGoogle Scholar
  126. I. Peschel, W. Dieterich: The diffusion of interacting classical particles as a many boson problem. Z. Phys. B 31, 195 (1978).ADSCrossRefGoogle Scholar
  127. H. Risken, H.D. Vollmer: Correlation functions for the diffusive motion of particles in a periodic potential. Z. Phys. B 31, 209 (1978).ADSCrossRefGoogle Scholar
  128. R. Zeyher: Hydrodynamics of superionic conductors. Z. Phys. B 31, 127 (1978).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

There are no affiliations available

Personalised recommendations