Theory of Atomic Motions in Simple Classical Liquids

K. S. Singwi; A. Sjölander

doi:10.1103/PhysRev.167.152

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Theory of Atomic Motions in Simple Classical Liquids

K. S. Singwi

A. Sjölander

Institute of Theoretical Physics, Sven Hultins gata, Göteborg, Sweden and Solid State Science Division, Argonne National Laboratory, Argonne, Illinois

Institute of Theoretical Physics, Sven Hultins gata, Göteborg, Sweden

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Phys. Rev. 167, 152 – Published 5 March, 1968

DOI: https://doi.org/10.1103/PhysRev.167.152

Abstract

This paper is an attempt towards developing a theory of the self-motion of atoms in monatomic classical fluids, based on a simplified Liouville equation and on a knowledge of the interaction potential $V (r)$ and the static pair correlation function $g (r)$ . A nonlinear integral equation for the velocity autocorrelation function $Φ (t)$ is derived which under certain approximations can be written as $\frac{d Φ (t)}{dt} + \int 0^{t} K (t - t^{'}) Φ (t^{'}) d t^{'} = 0$ where the kernel $K (t)$ is an implicit function of $Φ (t)$ . An expression for $K (t)$ in terms of $V (r)$ and $g (r)$ has been given. Explicit numerical calculations for the "memory" function $K (t)$ have been made for liquid argon at $T = 85.9 °$ K, and the results have been compared with those obtained by Rahman from his machine computations.

References (15)

P. A. Egelstaff, Rept. Progr. Phys. 29, 333 (1966) K. Sköld and K. E. Larsson, Phys. Rev. 161, 102 (1967) K. E. Larsson, in Thermal Neutron Scattering, edited by P. A. Egelstaff (Academic Press Inc., New York, 1965), p. 347
A. Rahman, Phys. Rev. 136, A405 (1964)
A. Sjölander, in Thermal Neutron Scattering, edited by P. A. Egelstaff (Academic Press Inc., New York, 1965), p. 291 V. F. Sears, Proc. Phys. Soc. (London), 86, 953 (1965) A. G. Gibbs, in Symposium on Inelastic Scattering of Neutrons by Condensed Systems (Brookhaven National Laboratory, Associated Universities, Inc., 1965), p. 155 V. Ardente, G. F. Nardelli, and L. Reatto, Phys. Rev. 148, 124 (1966) P. S. Damle, A. Sjölander, and K. S. Singwi, ibid. 165, 277 (1968)
B. J. Berne, J. P. Boon, and S. A. Rice, J. Chem. Phys. 45, 1086 (1966)
K. S. Singwi and M. P. Tosi, Phys. Rev. 157, 153 (1967)
R. Kubo, in Many-Body Theory, 1965 Tokyo Summer Lectures in Theoretical Physics, edited by R. Kubo (W. A. Benjamin, Inc., New York, 1966), Part I, p. 1
R. Zwanzig, in Lectures in Theoretical Physics, edited by W. E. Brittin (Interscience Publishers, Inc., New York, 1961), p. 106
H. Mori, Progr. Theoret. Phys. (Kyoto) 33, 423 (1965)
A. Rahman (unpublished)
M. Born and H. S. Green, Proc. Roy. Soc. (London) A188, 10 (1946) J. Yvon, in La Theorie Statistique des Fluides et l'Equation d'Etat (Hermann & Cie., Paris, 1935) N. N. Bogoliubov, J. Phys. USSR 10, 265 (1946) J. G. Kirkwood, J. Chem. Phys. 14, 180 (1946) E. G. D. Cohen, in Fundamental Problems in Statistical Mechanics (North-Holland Publishing Co., Amsterdam, 1962)
L. Van Hove, Phys. Rev. 95, 249 (1954)
G. H. Vineyard, Phys. Rev. 110, 999 (1958)
A. Rahman, K. S. Singwi, and A. Sjölander, Phys. Rev. 126, 986 (1962)
N. S. Gingrich and C. W. Tompson, J. Chem. Phys. 36, 2398 (1962)
B. R. A. Nijboer and A. Rahman, Physica 32, 415 (1966) P. Schofield, in Inelastic Scattering of Neutrons in Solids and Liquids (International Atomic Energy Agency, Vienna, 1961), p. 39

[c1] P. A. Egelstaff, Rept. Progr. Phys. 29, 333 (1966) K. Sköld and K. E. Larsson, Phys. Rev. 161, 102 (1967) K. E. Larsson, in Thermal Neutron Scattering, edited by P. A. Egelstaff (Academic Press Inc., New York, 1965), p. 347

[c2] A. Rahman, Phys. Rev. 136, A405 (1964)

[c3] A. Sjölander, in Thermal Neutron Scattering, edited by P. A. Egelstaff (Academic Press Inc., New York, 1965), p. 291 V. F. Sears, Proc. Phys. Soc. (London), 86, 953 (1965) A. G. Gibbs, in Symposium on Inelastic Scattering of Neutrons by Condensed Systems (Brookhaven National Laboratory, Associated Universities, Inc., 1965), p. 155 V. Ardente, G. F. Nardelli, and L. Reatto, Phys. Rev. 148, 124 (1966) P. S. Damle, A. Sjölander, and K. S. Singwi, ibid. 165, 277 (1968)

[c4] B. J. Berne, J. P. Boon, and S. A. Rice, J. Chem. Phys. 45, 1086 (1966)

[c5] K. S. Singwi and M. P. Tosi, Phys. Rev. 157, 153 (1967)

[c6] R. Kubo, in Many-Body Theory, 1965 Tokyo Summer Lectures in Theoretical Physics, edited by R. Kubo (W. A. Benjamin, Inc., New York, 1966), Part I, p. 1

[c7] R. Zwanzig, in Lectures in Theoretical Physics, edited by W. E. Brittin (Interscience Publishers, Inc., New York, 1961), p. 106

[c8] H. Mori, Progr. Theoret. Phys. (Kyoto) 33, 423 (1965)

[c9] A. Rahman (unpublished)

[c10] M. Born and H. S. Green, Proc. Roy. Soc. (London) A188, 10 (1946) J. Yvon, in La Theorie Statistique des Fluides et l'Equation d'Etat (Hermann & Cie., Paris, 1935) N. N. Bogoliubov, J. Phys. USSR 10, 265 (1946) J. G. Kirkwood, J. Chem. Phys. 14, 180 (1946) E. G. D. Cohen, in Fundamental Problems in Statistical Mechanics (North-Holland Publishing Co., Amsterdam, 1962)

[c11] L. Van Hove, Phys. Rev. 95, 249 (1954)

[c12] G. H. Vineyard, Phys. Rev. 110, 999 (1958)

[c13] A. Rahman, K. S. Singwi, and A. Sjölander, Phys. Rev. 126, 986 (1962)

[c14] N. S. Gingrich and C. W. Tompson, J. Chem. Phys. 36, 2398 (1962)

[c15] B. R. A. Nijboer and A. Rahman, Physica 32, 415 (1966) P. Schofield, in Inelastic Scattering of Neutrons in Solids and Liquids (International Atomic Energy Agency, Vienna, 1961), p. 39

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Theory of Atomic Motions in Simple Classical Liquids

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