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Atomic Motions in Liquids

  • Chapter
Amorphous and Liquid Materials

Part of the book series: NATO ASI Series ((NSSE,volume 118))

Abstract

At the Advanced NATO Study Institute at Zwiesel in 1979 I gave a few lectures on the atomic theory of liquid dynamics. The theory was based on the Zwanzig-Mori memory function approach. Since then the whole field has matured and we have seen some more applications of the theory. However, the conceptual ideas have not changed and I will here repeat several points, which I stressed at that time. This kind of theory can be viewed as a generalization both of the ordinary Boltzmann equation for dilute gases and of the Vlasov equation for classical plasmas. For both of them one introduces the density in the six-dimensional phase space, denoted by f\( (\vec{r}\vec{p}t) \). Its evolution in time is in the appropriate situations governed by these equations. The linearized version of the Vlasov equation reads

$$(\frac{\partial }{{\partial t}} + \frac{1}{m}\overrightarrow p \bullet \overrightarrow \triangledown r)f(\overrightarrow r \overrightarrow {pt} ) - \{ \int {d\overrightarrow r } \bullet d\overrightarrow p \bullet \overrightarrow \triangledown rv(\overrightarrow r - \overrightarrow r \bullet )f(\overrightarrow r \bullet \overrightarrow p \bullet t)\} \bullet \overrightarrow \triangledown p{f^{eq}}(p) = 0(1)$$
((1))

, where v(r) is the interparticle (Coulomb) potential, m is the particle mass, and \( {f^{{eq}}}(p) = n{\phi_M}(p) \) is the equilibrium distribution, with n being the uniform particle density and 4>M(p) the normalized Maxwellian momentum distribution. The linearized Boltzmann equation takes the form

$$(\frac{\partial }{{\partial t}} + \frac{1}{m}\overrightarrow p \bullet {\overrightarrow \triangledown _r})f(\overrightarrow r \overrightarrow p t) - \int d \overrightarrow p \bullet K(\overrightarrow p \overrightarrow p \bullet )f(\overrightarrow r \overrightarrow p t) = 0$$
((2))

with a kernel \( K(\vec{p},\vec{p}') \), which contains information on the effect of a single binary collision. The interaction between the particles enters in \( K(\vec{p},\vec{p}') \) through the binary collision cross section.

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References

  1. Lebowitz, J.L., Percus, J.K. and Sykes, J., Phys. Rev, 188, 487 (1969).

    Article  Google Scholar 

  2. Furtado, P.M., Mazenko, G.F. and Yip, S., Phys. Rev. A12, 1653 (1975).

    Google Scholar 

  3. Alley, W.E. and Alder, B.J., Phys. Rev. A27, 3158 (1983).

    Google Scholar 

  4. Alley, W.E., Alder, B.J., and Yip, S., Phys. Rev. A27, 3174 (1983).

    Google Scholar 

  5. Forster, D., Hydrodynamics, Fluctuations, Broken Symmetry, and Correlation Functions, W.A. Benjamin Inc., London, 1975.

    Google Scholar 

  6. Boon, J.P. and Yip, S., Molecular Hydrodynamics, McGraw-Hill, New York, 1980.

    Google Scholar 

  7. Sjögren, L., Ann. Phys. (N.Y.) 113, 304 (1978).

    Article  Google Scholar 

  8. Alder, B.J. and Wainwright, T.E., Phys. Rev. A1, 18 (1970).

    Google Scholar 

  9. Zwanzig, R. and Bixon, M., Phys. Rev. A2, 2005 (1970).

    Google Scholar 

  10. Akcasu, A.Z. and Duderstadt, J.J., Phys. Rev. 188, 479 (1969)

    Article  Google Scholar 

  11. Akcasu, A.Z. and Duderstadt, J.J., Phys. Rev. Al, 905 (1969).

    Google Scholar 

  12. Forster, D. and Martin, P.C., Phys. Rev. A2, 1575 (1970).

    Google Scholar 

  13. Mazenko, G.F., Phys. Rev. 7, 209, 222 (1973)

    Article  Google Scholar 

  14. Mazenko, G.F., Phys. Rev. A9, 360 (1974).

    Google Scholar 

  15. Mazenko, G.F., Phys. Rev. A6, 2545 (1972).

    Google Scholar 

  16. Zwanzig, R., J. Chem. Phys. 33, 1338 (1960)

    CAS  Google Scholar 

  17. Zwanzig, R. Phys. Rev. 124, 983 (1961).

    Article  CAS  Google Scholar 

  18. Mori, H., Progr. Theor. Phys. 34, 399 (1965).

    Article  Google Scholar 

  19. Forster, D., Phys. Rev. A9, 943 (1974).

    Google Scholar 

  20. Egelstaff, P.A., An Introduction to the Liquid State, Academic Press New York, 1967.

    Google Scholar 

  21. Ailawadi, K.N., Rahman, A. and Zwanzig, R., Phys. Rev. A4, 1616 (1971).

    Google Scholar 

  22. Sjödin, S. and Sjölander, A., Phys. Rev. A18, 1723 (1978).

    Google Scholar 

  23. Leutheusser, E., J. Phys. C: Solid State Phys. 15, 2827 (1982).

    Article  CAS  Google Scholar 

  24. Sjögren, L., Phys. Rev. A22, 2866 (1980)

    Google Scholar 

  25. Götze, W. and Lücke, M., Phys. Rev. A11, 2173 (1975)

    Google Scholar 

  26. Bosse, J., Götze, W. and Lücke, M., Phys. Rev. A17, 434, 447 (1978)

    Google Scholar 

  27. Bosse, J., Götze, W. and Lücke, M. Phys. Rev. A18, 1176 (1978).

    Google Scholar 

  28. Sjögren, L. and Sjölander, A., J. Phys. C: Solid State Phys. 12, 4369 (1979).

    Article  Google Scholar 

  29. Ernst, M.H. and Dorfmann, J.R., Physica (Utrecht) 61, 157 (1972).

    Article  Google Scholar 

  30. Feynman, R.P. and Cohen, M., Phys. Rev. 102, 1189 (1956)

    Article  Google Scholar 

  31. Cukier, R.I. and Mehaffey, J.R., Phys. Rev. A18, 1202 (1978).

    Google Scholar 

  32. Leutheusser, E., J. Phys. C: Solid State Phys. 12, 2801 (1982).

    Article  Google Scholar 

  33. Cukier, R.I., Mehaffey, J.R. and Kapral, R., J. Chem. Phys. 69, 4962 (1978)

    Article  CAS  Google Scholar 

  34. Cukier, R.I., Mehaffey, J.R. and Kapral, R., J. Chem. Phys. 74, 2494 (1980).

    Article  Google Scholar 

  35. Sung, W. and Dahler, J.S., J. Chem. Phys. 78, 6264, 6280 (1983).

    Article  CAS  Google Scholar 

  36. Sjogren, L. and Yoshida, F., J. Chem. Phys. 77, 3703 (1982)

    Article  Google Scholar 

  37. Bosse, J. and Munakata, T., Phys. Rev. A25, 2763 (1982).

    Google Scholar 

  38. Larsson, K.E., Phys. Chem. Liq. 12, 273 (1983).

    Article  CAS  Google Scholar 

  39. Sjogren, L., Phys. Rev. A22, 2883 (1980)

    Google Scholar 

  40. Larsson, K.E., preprint.

    Google Scholar 

  41. Balucani, U., Vallauri, R., Murthy, CS., Gaskell, T. and Woolfson, M.S., J. Phys. C: Solid State Phys. 16, 5605 (1983).

    Article  CAS  Google Scholar 

  42. Sjögren, L., J. Phys. C: Solid State Phys. 13, 705 (1980).

    Article  Google Scholar 

  43. Tanaka, M., Progr. Theor. Phys. Suppl. 69, 439 (1980).

    Article  CAS  Google Scholar 

  44. Nijboer, B.R.A. and Rahman, A., Physica 32, 415 (1966).

    Article  Google Scholar 

  45. Levesque, D., and Verlet, L., Phys. Rev. A2, 2514 (1970).

    Google Scholar 

  46. Wahnström, G. and Sjögren, L., J. Phys. G; Solid State Phys. 15, 401 (1982).

    Article  Google Scholar 

  47. De Shepper, I.M., Van Beyeren, H. and Ernst, M.H., Physica 75, 1 (1974)

    Article  Google Scholar 

  48. see also Verkerk, P., Builtjes, J.H. and de Schepper, I.M., Phys. Rev. A31, 1731 (1985).

    Google Scholar 

  49. Kadanoff, L.P. and Swift, J., Phys. Rev. 166, 89 (1968).

    Article  CAS  Google Scholar 

  50. Kawasaki, K., Phys. Rev. 150, 291 (1966); Ann. Phys. (N.Y.) 61, 1 (1970).

    Article  CAS  Google Scholar 

  51. Kawasaki, Ann. Phys. (N.Y.) 61, 1 (1970).

    Article  CAS  Google Scholar 

  52. Sjölander, A. and Turski, L.A., J. Phys. C: Solid State Phys. 11, 1973 (1978).

    Article  Google Scholar 

  53. Leutheusser, E., Phys. Rev. A29, 2765 (1984).

    Google Scholar 

  54. Bengtzelius, U., Götze, W. and Sjölander A., J. Phys. C: Solid State Phys. 17, 5915 (1984).

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, S-412 96, Göteborg, Sweden

    Alf Sjölander

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  1. Alf Sjölander
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Editors and Affiliations

  1. Physik-Department, Technische Universität München, D-8046, Garching, Germany

    E. Lüscher

  2. Physikalisches Institut FB BAUV/II, Universität der Bundeswehr München, D-8014, Neubiberg, Germany

    G. Fritsch

  3. Dipartimento di Matematica e Fisica, Universita degli Studi di Trento, I-38050, Povo, Italy

    G. Jacucci

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© 1987 Martinus Nijhoff Publishers, Dordrecht

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Sjölander, A. (1987). Atomic Motions in Liquids. In: Lüscher, E., Fritsch, G., Jacucci, G. (eds) Amorphous and Liquid Materials. NATO ASI Series, vol 118. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3505-1_19

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  • DOI: https://doi.org/10.1007/978-94-009-3505-1_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8066-8

  • Online ISBN: 978-94-009-3505-1

  • eBook Packages: Springer Book Archive

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