Self-Motion in Liquids

Part of the Physics of Solids and Liquids book series (PSLI)

Abstract

The aim of this chapter is to outline the principal methods used to describe atomic motions in monatomic liquids like rare-element liquids, or liquid metals within the adiabatic approximation. We shall be mainly concerned with the self-motion of a tagged particle immersed in a fluid, but the general methods presented can on the whole be applied when studying the dynamics of the fluid itself.

Keywords

Friction Coefficient Memory Function Diffusion Constant Langevin Equation Velocity Autocorrelation Function 
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.

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References

  1. 1.
    N. H. March, in: Theory of Condensed Matter, p. 93, I. A. E. A., Vienna (1968).Google Scholar
  2. 2.
    J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, New York (1976).Google Scholar
  3. 3.
    J. P. Hansen, in: Microscopic Structure and Dynamics of Liquids (J. Dupuy and A. J. Dianoux, eds.), Vol. 33, p. 3, Nato Advanced Study Institutes Series. Plenum Press, New York (1978).Google Scholar
  4. 4.
    K. Sköld, J. M. Rowe, G. Ostrowski, and P. D. Randolph, Phys. Rev. A 6, 1107 (1972).CrossRefGoogle Scholar
  5. 5.
    J. R. D. Copley and S. W. Lovesey, Rep. Prog. Phys. 38, 461 (1975).CrossRefGoogle Scholar
  6. 6.
    P. A. Egelstaff and P. Schofield, Nucl. Sci. Eng. 12, 260 (1962).Google Scholar
  7. 7.
    D. Levesque, L. Verlet, and J. Kurkijärvi, Phys. Rev. A 7, 1690 (1973).CrossRefGoogle Scholar
  8. 8.
    S. W. Lovesey, J. Phys. C 6, 1856 (1973).CrossRefGoogle Scholar
  9. 9.
    S. W. Lovesey, in: Dynamics of Solids and Liquids by Neutron Scattering ( S. W. Lovesey and T. Springer, eds.), Springer-Verlag, Berlin (1977).CrossRefGoogle Scholar
  10. 10.
    B. R. A. Nijboer and A. Rahman, Physica 32, 415 (1966).Google Scholar
  11. 11.
    P. Schofield, Proc. I. A. E. A. Symposium, p. 39, Vienna (1961).Google Scholar
  12. 12.
    D. Levesque and L. Verlet, Phys. Rev. A 2, 2514 (1970).CrossRefGoogle Scholar
  13. 13.
    A. Rahman, Phys. Rev. A 136, 405 (1964).Google Scholar
  14. 14.
    B. J. Alder and T. E. Wainwright, Phys. Rev. Leu. 18, 988 (1967).CrossRefGoogle Scholar
  15. B. J. Alder and T. E. Wainwright, J. Phys. Soc. Jpn., Suppl. 26, 267 (1968).Google Scholar
  16. B. J. Alder and T. E. Wainwright, Phys. Rev. A 1, 18 (1970).CrossRefGoogle Scholar
  17. B. J. Alder, D. M. Gass, and T. E. Wainwright, J. Chem. Phys. 53, 3813 (1970).CrossRefGoogle Scholar
  18. B. J. Alder, W. E. Alley, and J. H. Dymond, J. Chem. Phys. 56, 987 (1972)CrossRefGoogle Scholar
  19. B. J. Alder, W. E. Alley, and J. H. Dymond, J. Chem. Phys. 61, 1415 (1974).CrossRefGoogle Scholar
  20. 15.
    K. Toukubo and K. Nakanishi, J. Chem. Phys. 65, 1937 (1976).CrossRefGoogle Scholar
  21. 16.
    J. P. Hansen and I. R. McDonald, Phys. Rev. A 11, 2111 (1975).CrossRefGoogle Scholar
  22. 17.
    G. Jacucci and I. R. McDonald, Physica A 80, 607 (1975).CrossRefGoogle Scholar
  23. 18.
    I. Ebbsjö, P. Schofield, K. Sköld, and I. Waller, J. Phys. C 7, 3891 (1974).CrossRefGoogle Scholar
  24. 19.
    M. Parrinello, M. P. Tosi, and N. H. March, J. Phys. C 7, 2577 (1974).CrossRefGoogle Scholar
  25. 20.
    A. Einstein, Ann. Physik 17, 549 (1905)CrossRefGoogle Scholar
  26. A. Einstein, Ann. Physik 19, 371 (1906).CrossRefGoogle Scholar
  27. P. Langevin, C. R. Acad. Sci. Paris 146, 530 (1908).Google Scholar
  28. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).CrossRefGoogle Scholar
  29. 21.
    L. S. Ornstein and W. R. van Wijk, Physica 1, 235 (1933).CrossRefGoogle Scholar
  30. 22.
    S. A. Rice and P. Gray, The Statistical Mechanics of Simple Liquids, Monographs in Statistical Physics, Vol. 3, Interscience Publ., New York (1965).Google Scholar
  31. 23.
    Ph. Noziéres, Lecture Notes, Grenoble University (unpublished).Google Scholar
  32. 24.
    J. Lebowitz and E. Rubin, Phys. Rev. 131, 2381 (1963).CrossRefGoogle Scholar
  33. 25.
    P. Résibois and H. T. Davis, Physica 30, 1077 (1964).CrossRefGoogle Scholar
  34. 26.
    J. G. Kirkwood, J. Chem. Phys. 14, 180 (1946).CrossRefGoogle Scholar
  35. 27.
    G. Boato, G. Casanova, and A. Levi, J. Chem. Phys. 40, 2419 (1964).CrossRefGoogle Scholar
  36. 28.
    J. A. Palyvos and H. T. Davis, J. Phys. Chem. 71, 439 (1967).CrossRefGoogle Scholar
  37. 29.
    H. T. Davis and J. A. Palyvos, J. Chem. Phys. 46, 4043 (1967).CrossRefGoogle Scholar
  38. 30.
    R. V. Gopala Rao and A. K. Murthy, Z. Naturforsch. 30a, 619 (1975).Google Scholar
  39. 31.
    K. Ichikawa and M. Shimoji, Phil. Mag. 20, 341 (1969).CrossRefGoogle Scholar
  40. 32.
    E. Helfand, Phys. Fluids 4, 681 (1961).CrossRefGoogle Scholar
  41. 33.
    S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, New York (1958).Google Scholar
  42. 34.
    H. C. Longuet-Higgins and J. A. Pople, J. Chem. Phys. 25, 884 (1956).CrossRefGoogle Scholar
  43. 35.
    S. A. Rice, J. G. Kirkwood, J. Ross, and R. W. Zwanzig, J. Chem. Phys. 31, 575 (1959).CrossRefGoogle Scholar
  44. 36.
    J. T. O’Toole and J. S. Dahler, J. Chem. Phys. 33, 1496 (1960).CrossRefGoogle Scholar
  45. 37.
    G. C. Stokes, Trans. Camb. Phil. Soc. 8, 287 (1845).Google Scholar
  46. J. Boussinesq, J. Math. Pures Appl. (2) 13, 377 (1868).Google Scholar
  47. Barré de Saint Venant, C. R. Acad. Sci. Paris 17, 1240 (1843).Google Scholar
  48. 38.
    R. Zwanzig and M. Bixon, Phys. Rev. A 2, 2005 (1970).CrossRefGoogle Scholar
  49. 39.
    A. Rahman, J. Chem. Phys. 45, 2585 (1966).CrossRefGoogle Scholar
  50. 40.
    J. R. Dorfman and E. G. D. Cohen, Phys. Rev. Lett. 25, 1257 (1970)CrossRefGoogle Scholar
  51. J. R. Dorfman and E. G. D. Cohen, Phys. Rev. A 6, 776 (1972)CrossRefGoogle Scholar
  52. J. R. Dorfman and E. G. D. Cohen, Phys. Rev. A 12, 292 (1975).CrossRefGoogle Scholar
  53. 41.
    M. H. Ernst, E. H. Hauge, and J. M. J. van Leeuwen, Phys. Rev. Lett. 25, 1254 (1970)CrossRefGoogle Scholar
  54. M. H. Ernst, E. H. Hauge, and J. M. J. van Leeuwen, Phys. Rev. A 4, 2055 (1971).CrossRefGoogle Scholar
  55. 42.
    D. Levesque and W. T. Ashurst, Phys. Rev. Lett. 33, 277 (1974).CrossRefGoogle Scholar
  56. 43.
    B. J. Berne, J. P. Boon, and S. A. Rice, J. Chem. Phys. 45, 1086 (1966).CrossRefGoogle Scholar
  57. 44.
    G. D. Harp and B. J. Berne, Phys. Rev. A 2, 975 (1970).CrossRefGoogle Scholar
  58. 45.
    K. Singwi and S. Tosi, Phys. Rev. 157, 153 (1967).CrossRefGoogle Scholar
  59. 46.
    P. Martin and S. Yip, Phys. Rev. 170, 151 (1968).CrossRefGoogle Scholar
  60. 47.
    R. Desai and S. Yip, Phys. Rev. 166, 129 (1968).CrossRefGoogle Scholar
  61. 48.
    R. Zwanzig, in: Molecular Fluids ( R. Balian and G. Weill, eds.), Gordon and Breach, London (1973).Google Scholar
  62. 49.
    H. Mori, Prog. Theor. Phys. 33, 423 (1965).CrossRefGoogle Scholar
  63. 50.
    H. Mori, Prog. Theor. Phys. 34, 399 (1965).CrossRefGoogle Scholar
  64. 51.
    J. Bosse, W. Götze, and M. Lücke, Phys. Rev. A 17, 434 (1978)CrossRefGoogle Scholar
  65. J. Bosse, W. Götze, and M. Lücke, Phys. Rev. A. 17, 447 (1978).CrossRefGoogle Scholar
  66. 52.
    A. Zippelius and W. Götze, Phys. Rev. A 17, 414 (1978).CrossRefGoogle Scholar
  67. 53.
    J. Bosse, W. Götze, and M. Lücke, Phys. Rev. A 18, 1176 (1978).CrossRefGoogle Scholar
  68. 54.
    J. Bosse, W. Götze, and A. Zippelius, Phys. Rev. A 18, 1214 (1978).CrossRefGoogle Scholar
  69. 55.
    T. Munakata and I. Igarashi, Prog. Theor. Phys. 58, 1345 (1977)CrossRefGoogle Scholar
  70. T. Munakata and I. Igarashi, Prog. Theor. Phys. 60, 45 (1978).CrossRefGoogle Scholar
  71. 56.
    G. S. Dubey, V. K. Jindal, and K. N. Pathak, Prog. Theor. Phys. 64, 1893 (1980).CrossRefGoogle Scholar
  72. 57.
    B. F. McCoy, Phys. Rev. A 12, 1678 (1975).CrossRefGoogle Scholar
  73. 58.
    P. Résibois and M. de Leener, Classical Kinetic Theory of Fluids, John Wiley and Sons, New York (1977).Google Scholar
  74. 59.
    S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, New York (1970).Google Scholar
  75. 60.
    J. H. Dymond and B. J. Alder, J. Chem. Phys. 48, 343 (1968).CrossRefGoogle Scholar
  76. J. H. Dymond, Physica 75, 100 (1974).CrossRefGoogle Scholar
  77. J. H. Dymond, J. Chem. Phys. 60, 969 (1972).CrossRefGoogle Scholar
  78. 61.
    P. Ascarelli and A. Paskin, Phys. Rev. B 165, 222 (1968).CrossRefGoogle Scholar
  79. 62.
    C. J. Vadovic and C. P. Colver, Phys. Rev. B 1, 4850 (1970).CrossRefGoogle Scholar
  80. 63.
    N. F. Carnahan and K. E. Starling, J. Chem. Phys. 51, 635 (1969).CrossRefGoogle Scholar
  81. 64.
    L. Verlet and J. J. Weis, Phys. Rev. A 5, 939 (1971).CrossRefGoogle Scholar
  82. 65.
    P. Protopapas, H. C. Andersen, and N. A. D. Parlee, J. Chem. Phys. 59, 15 (1973).CrossRefGoogle Scholar
  83. P. Protopapas and N. A. D. Parlee, J. Chem. Phys. 11, 201 (1975).Google Scholar
  84. P. Protopapas and N. A. D. Parlee, High Temp. Sci. 7, 259 (1975).Google Scholar
  85. 66.
    K. S. Singwi and A. Sjölander, Phys. Rev. A 167, 152 (1968).Google Scholar
  86. K. S. Singwi, in: Theory of Condensed Matter, p. 603, I.A.E.A., Vienna (1968).Google Scholar
  87. 67.
    A. Z. Akcasu and E. Daniels, Phys. Rev. A 2, 962 (1970).CrossRefGoogle Scholar
  88. A. Z. Akcasu and J. J. Duderstadt, Phys. Rev. 188, 479 (1969).CrossRefGoogle Scholar
  89. 68.
    J. L. Lebowitz, J. K. Percus, and J. Sykes, Phys. Rev. 188, 487 (1969).CrossRefGoogle Scholar
  90. 69.
    P. Résibois and J. L. Lebowitz, J. Stat. Phys. 12, 483 (1975).CrossRefGoogle Scholar
  91. P. Résibois, J. Stat. Phys. 13, 393 (1975).CrossRefGoogle Scholar
  92. Y. Pomeau and P. Résibois, Phys. Rep. C 19, 63 (1975).CrossRefGoogle Scholar
  93. 70.
    C. D. Boley, Ann. Phys. 86, 91 (1974)CrossRefGoogle Scholar
  94. C. D. Boley, Phys. Rev. A 11, 328 (1975).CrossRefGoogle Scholar
  95. 71.
    E. P. Gross, J. Stat. Phys. 11, 503 (1974)CrossRefGoogle Scholar
  96. E. P. Gross, J. Stat. Phys. 15, 181 (1976).CrossRefGoogle Scholar
  97. 72.
    L. Sjögren and A. Sjölander, Ann. Phys. 110, 122 (1978)CrossRefGoogle Scholar
  98. L. Sjögren and A. Sjölander, Ann. Phys. 110, 421 (1978)CrossRefGoogle Scholar
  99. L. Sjögren and A. Sjölander, J. Phys. C 12, 4369 (1979).CrossRefGoogle Scholar
  100. L. Sjögren, Ann. Phys. 110, 156 (1978)CrossRefGoogle Scholar
  101. L. Sjögren, Ann. Phys. 110, 173 (1978)CrossRefGoogle Scholar
  102. L. Sjögren, Ann. Phys. 113, 304 (1978)CrossRefGoogle Scholar
  103. L. Sjögren, J. Phys. C 11, 1493 (1978)CrossRefGoogle Scholar
  104. L. Sjögren, J. Phys. C 13, 705 (1980).CrossRefGoogle Scholar
  105. A. Sjölander, in: Liquid and Amorphous Metals (E. Lüscher and H. Coufal, eds.), p. 63, Nato Advanced Study Institutes Series, Vol. 36, Sijthoff and Noordhoff International Publishers B.V., Alphen aan den Rijn, The Netherlands (1980).Google Scholar
  106. 73.
    G. F. Mazenko, Phys. Rev. A 7, 209 (1973)CrossRefGoogle Scholar
  107. G. F. Mazenko, Phys. Rev. A 7, 222 (1973)CrossRefGoogle Scholar
  108. G. F. Mazenko, Phys. Rev. A 9, 360 (1974).CrossRefGoogle Scholar
  109. P. M. Furtado, G. F. Mazenko, and S. Yip, Phys. Rev. A 12, 1653 (1975).CrossRefGoogle Scholar
  110. J. R. Mehaffey, R. C. Desai, and R. Kapral, J. Chem. Phys. 66, 1665 (1977).CrossRefGoogle Scholar
  111. J. R. Mehaffey and R. I. Cukier, Phys. Rev. A 17, 1181 (1978).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • M. Gerl
    • 1
  1. 1.Laboratoire de Physique du Solide (L.A. au C.N.R.S. n° 155)Faculté des SciencesVandoeuvre Les Nancy CedexFrance

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