HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 41 (1969) > Number 2
| Next Article >

Prog. Theor. Phys. Vol. 41 No. 2 (1969) pp. 285-295

[ Full Text PDF : FREE ACCESS (667K) ]

Kinetic Theory of Collective Modes in Classical Liquids

Junzo Chihara

Japan Atomic Energy Research Institute, Tokai-Mura, Ibaraki-Ken

(Received July 13, 1968)

Abstract:

By solving the linearized Vlasov-Boltzmann equation it is shown that zero sound can exist in classical liquids. The effective interatomic potential is shown to be expressed in terms of the direct correlation function. The real and imaginary parts of the frequency are expressed analytically for both small and large values of wave-vector k, but in general are obtained numerically. In our solution of the dispersion relation, first (ordinary) sound and zero sound originate from the same pole; the former is the solution for smaller k and the latter is that for large k. We believe that the collective modes observed in classical liquids by neutron scattering experiments should be interpreted as zero sound. The imaginary part of the diffusion pole which contributes to the line width of the quasi-elastic peak, becomes small for the wave-vector where the form factor S(k) has peaks.


URL : http://ptp.ipap.jp/link?PTP/41/285/
DOI : 10.1143/PTP.41.285

[ Full Text PDF : FREE ACCESS (667K) ] Citation:

References:

  1. S. J. Cooking and P. A. Egelstaff, Phys. Lett. 16 (1965), 30[CrossRef].
    S. H. Chen et al., Phys. Lett. 19 (1965), 269[CrossRef].
    S. J. Cooking, Adv. in Phys. 16 (1967), 189.
  2. P. G. de Gennes, Physica 25 (1959), 825[CrossRef].
  3. A. A. Vlasov, Many-Particle Theory and Its Application to Plasma, 1950 (English Transl: Gordon and Breach, 1961), chap. 4.
  4. Y. Klimontovich and V. P. Silin, Uspekhi Fiz. Nauk SSSR 70 (1960), 247.
  5. N. Takimoto and B. W. Ninham, Prog. Theor. Phys. 32 (1964), 8[PTP].
  6. M. Nelkin and S. Ranganathan, Phys. Rev. 164 (1967), 222[APS].
  7. S. A. Rice and P. Gray, The Statistical Mechanics of Simple Liquids (Interscience Publisher, 1965), chap. 5.
  8. N. Hashitsume, Prog. Theor. Phys. 15 (1956), 369[PTP].
  9. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, 1958), chap. 12.
  10. P. L. Bhatnager, E. P. Gross and M. Krook, Phys. Rev. 94 (1954), 511[APS].
  11. A. G. Sitenko and A. A. Gurin, Zh. Eksp. Teor. Fiz. 49 (1965), 1591 (English Transl: Sov. Phys. -JETP 22 (1966), 1089).
  12. N. D. Mermin, Ann. of Phys. 18 (1962), 421[CrossRef].
  13. R. Aronson, J. Math. Phys. 7 (1966), 589[CrossRef].
  14. R. Zwanzig, Phys. Rev. 144 (1966), 170[APS].
  15. N. Ashcroft, Physica 35 (1967), 148[CrossRef].
  16. B. A. Dasannacharya and K. R. Rao, Phys. Rev. 137 (1965), A417[APS].
    G. Venkataraman et al., Phys. Rev. 161 (1967), 133[APS].
  17. W. R. Abel et al., Phys. Rev. Lett. 17 (1966), 74[APS].
  18. P. A. Egelstaff, Rep. Prog. Theor. Phys. 29 (1966), 333[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 45 No. 2 (1971) pp. 331-352 :
    A Theory of Phonons in Amorphous Solids and Its Implications to Collective Motion in Simple Liquids
    Shozo Takeno and Masaki Gôda
  2. Progress of Theoretical Physics Vol. 47 No. 2 (1972) pp. 395-415 :
    A Generalization of the Hartree Approximation and the Quantal Space-Time Correlation Function
    Junzo Chihara
  3. Progress of Theoretical Physics Vol. 47 No. 3 (1972) pp. 790-806 :
    A Theory of Phonon-Like Excitations in Non-Crystalline Solids and Liquids
    Shozo Takeno and Masaki Goda
  4. Progress of Theoretical Physics Vol. 48 No. 3 (1972) pp. 724-730 :
    Phonon-Like Excitations in Liquid Helium
    Shozo Takeno and Masaki Goda
  5. Progress of Theoretical Physics Vol. 50 No. 1 (1973) pp. 1-16 :
    Wave Number Dependence of the Relaxation Time for the Longitudinal Mode in Simple Liquid
    Mitsunobu Machida and Chiaki Murase
  6. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 409-423 :
    Integral Euqations for Fluids with Long-Range and Short-Range Potentials
    Junzo Chihara
  7. Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 794-806 :
    Space-Time Correlation Functions in Quantal and Classical Binary Mixtures. I
    Junzo Chihara
  8. Progress of Theoretical Physics Vol. 50 No. 4 (1973) pp. 1156-1181 :
    Integral Equations for Neutral and Charged Quantum Fluids Including Extension of the Percus-Yevick Equation
    Junzo Chihara
  9. Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 293-304 :
    High-Frequency Expansion of Memory Function in Classical Simple Liquids
    Fukuo Yoshida and Shozo Takeno
  10. Progress of Theoretical Physics Vol. 62 No. 4 (1979) pp. 883-900 :
    Dynamical Structure Factor and Collective Modes in Classical One-Component Plasmas
    Shozo Takeno and Fukuo Yoshida

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.