Light Scattering Determinations of Dynamic Four Point Correlation Functions

  • P. A. Fleury
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 35)


For many purposes the dynamics of a many body system are adequately described by the familiar autocorrelation function \( S\left( {\vec q,w} \right) \). \( S\left( {\vec q,w} \right) \) is the Fourier transform of \(\left\langle {u\left( {\vec r,t} \right)u\left( {\vec r't'} \right)} \right\rangle\), where \(u\left( {\vec r,t} \right)\) represents some characteristic dynamic variable such as spin, density, etc. Scattering experiments using light, neutrons, electrons or x-rays, are routinely directed toward the measurement of \( S\left( {\vec q,w} \right) \). However in recent years it has become increasingly appreciated that such scattering probes may also couple strongly to higher powers of the dynamic variable and may thus explore more complex dynamic correlation functions than \( S\left( {\vec q,w} \right) \). Indeed the operation of certain selection rules, particularly for light scattering, often permits rather direct and unambiguous measurement of the four point correlation function \( \left\langle {u\left( {{{\vec r}_1}{t_1}} \right)u\left( {{{\vec r}_2}{t_2}} \right)u\left( {{{\vec r}_3}{t_3}} \right)u\left( {{{\vec r}_4}{t_4}} \right)} \right\rangle \). This type of function contains information on the interactions among those elementary excitations, which are described to lowest order by \( S\left( {\vec q,w} \right) \). In addition, various limits of this function determine such quantities as specific heat, acoustic attenuation, and other transport properties.


Correlation Function Spin Hamiltonian Parameter Para Hydrogen Point Correlation Function Spin Correlation Function 
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  1. 1.
    See for example, R. Loudon, Adv. in Phys. 17, 243, 1968.ADSCrossRefGoogle Scholar
  2. 2.
    P. A. Fleury, Proc. Int’l. Conf. on Magnetism, Vol. 1, Nauka, Moscow, 1974, P. 80.Google Scholar
  3. 3.
    T. Moriya, J. Appl. Phys. 39, 1042 (1968).ADSCrossRefGoogle Scholar
  4. 4.
    P. A. Fluery and R. Loudon, Phys. Rev. l66, 514 (1968).CrossRefGoogle Scholar
  5. 5.
    P. A. Fleury, S. P. S. Porto, L. E. Cheesman and H. J. Guggenheim, Phys. Rev. Letters 17, 84, 1966.ADSCrossRefGoogle Scholar
  6. 6.
    S. R. Chinn, R. W. Davies, H. J. Zeiger, A.I.P. Conf. Proceedings #5 Magnetism and Magnetic Materials, ed. “by C. D. Graham and J. J. Rhyne 1972, p. 317.Google Scholar
  7. 7.
    Y. A. Popkov, V. I. Fomin and B. V. Beznosikov, JETP Lett. 11, 264 1970.ADSGoogle Scholar
  8. 8.
    P. A. Fleury, Int’l. J. Magnetism, 1, 75, 1970.Google Scholar
  9. 9.
    P. Moch et al., “Light Scattering in Solids”, edited by M. Balkanski, Flammarion, Paris, 1971, p. 138.Google Scholar
  10. 10.
    R. M. McFarlane, Phys. Rev. Lett. 25, 1454, 1970.ADSCrossRefGoogle Scholar
  11. 11.
    R. V. Pisarev, P. Moch and C. Dugautier, Phys. Rev. B7, 1185, 1973.Google Scholar
  12. 12.
    P. A. Fleury, Phys. Rev. 180, 591, 1969.ADSCrossRefGoogle Scholar
  13. 13.
    R. J. Elliott and M. F. Thorpe, J. Phys. C2, 1630, 1969, and this volume.ADSGoogle Scholar
  14. 14.
    M. F. Thorpe, Phys. Rev. B2, 2690, 1970.ADSGoogle Scholar
  15. 15.
    J. B. Parkinson, J. Phys. C2, 2012, 1969.ADSGoogle Scholar
  16. 16.
    P. A. Fleury and K. J. Guggenheim, Phys. Rev. Lett. 24, 1346, 1970.ADSCrossRefGoogle Scholar
  17. 17.
    P. A. Fleury in Ref. 9, p.151; R. Loudon, J. Phys. C3, 872, 1970;ADSGoogle Scholar
  18. 17a.
    M. G. Cottam, J. Phys. C8, 1933, 1975.ADSGoogle Scholar
  19. 18.
    C. R. Natoli and J. Ranninger, J. Phys. C6, 345, 1973.ADSGoogle Scholar
  20. 19.
    U. Balucani and V. Tognetti, P.R. B8, 4247, 1973Google Scholar
  21. 19a.
    U. Balucani and V. Tognetti, Rivista del Nuovo Cimento 6, 39, 1976.ADSCrossRefGoogle Scholar
  22. 20.
    Bohnen, C. R. Natoli and J. Ranninger, J. Phys. C7, 947, 1974.ADSGoogle Scholar
  23. 21.
    A. van der Pol et al., Solid State Comm. 19, 177, 1976.ADSCrossRefGoogle Scholar
  24. 22.
    U. Balucani and V. Tognetti, Phys. Rev. B_, 1977 in press.Google Scholar
  25. 23.
    S. Lovesey and R. Meserve, J. Phys. C6, 79, 1973.ADSGoogle Scholar
  26. 24.
    M. Buchanan, et al., J. Phys. C5, 2011, 1972.ADSGoogle Scholar
  27. 25.
    P. A. Fleury, W. Hayes and H. J. Guggenheim, J. Phys. C8, 2183, 1975.ADSGoogle Scholar
  28. 26.
    J. Als Nielsen, R. J. Birgeneau, H. J. Guggenheim, G. Shirane, Phys. Rev. B12, 4963, 1975.ADSGoogle Scholar
  29. 27.
    P. A. Fleury and H. J. Guggenheim, Phys. Rev. B12, 985, 1975.ADSGoogle Scholar
  30. 28.
    J. W. Halley, Light Scattering Spectra of Solids, edited by G. B. Wright, Springer-Verlag, New York, 1969, p. 177Google Scholar
  31. 29.
    M. J. Stephen, Phys. Rev. 187, 279, 1969.ADSCrossRefGoogle Scholar
  32. 30.
    H. B. Levine and G. Birnbaum, Phys. Rev. Lett. 20, 139, 1968.ADSGoogle Scholar
  33. 31.
    For a review see W. M. Gelbart, Adv. Chem. Phys. 26, 1, 1974.CrossRefGoogle Scholar
  34. 32.
    J. P. McTague, and G. Birnbaum, Phys. Rev. Lett. 21, 66l, 1968ADSCrossRefGoogle Scholar
  35. 32a.
    J. P. McTague, and G. Birnbaum, Phys. Rev., A3, 1376, 1971.ADSGoogle Scholar
  36. 33.
    P. A. Fleury and J. P. McTague, Optica Comm. 1, 164, 1969ADSCrossRefGoogle Scholar
  37. 33a.
    J. P. McTague, P. A. Fleury and D. R. DuPre, Phys. Rey. 188, 303, 1969.ADSCrossRefGoogle Scholar
  38. 34.
    T. J. Greytak and J. Yan, Phys. Rev. Lett. 22, 987, 1969.ADSCrossRefGoogle Scholar
  39. 35.
    P. A. Fleury, W. B. Daniels and J. M. Worlock, Phys. Rev. Lett. 27, 1493, 1971.ADSCrossRefGoogle Scholar
  40. 36.
    P. A. Fleury, J. M. W. Worlock and H. L. Carter, Phys. Rev. Lett. 30, 591, 1973.ADSCrossRefGoogle Scholar
  41. 37.
    B. J. Alder, H. L. Strauss and J. J. Weiss, J. Chem. Phys. 59, 1002, 1973.ADSCrossRefGoogle Scholar
  42. 38.
    N. R. Werthamer, R. L. Gray and T. R. Koehler, Phys. Rev. B2, 4199, 1970.ADSGoogle Scholar
  43. 39.
    R. W. Hellwarth, A. Owyoung and N. George, P.R. A4, 2342, 1971.Google Scholar
  44. 40.
    C.M. Surko and R. E. Slusher, Phys. Rev. B13, 1095, 1976.ADSGoogle Scholar
  45. 41.
    P. A. Fleury and J. P. McTague, Phys. Rev. Lett. 31, 914, 1973.ADSCrossRefGoogle Scholar
  46. 42.
    K. Carneiro, M. Nielsen, and J. P. McTague, Phys. Rev. Lett. 30, 481, 1973.ADSCrossRefGoogle Scholar
  47. 43.
    P. A. Fleury and J. P. McTague, Phys. Rev. A12, 317, 1975.ADSGoogle Scholar
  48. 44.
    I. Silvera, this proceedings.Google Scholar
  49. 45.
    See for example, R. K. Wehner and R. Klein, Physica 62, 161, 1972;ADSCrossRefGoogle Scholar
  50. 45a.
    G. J. Coombs and R. A. Cowley, J. Phys. C6, 121, 1973.ADSGoogle Scholar
  51. 46.
    K. B. Lyons and P. A. Fleury, Phys. Rev. Lett. 37, 161, 1976.ADSCrossRefGoogle Scholar
  52. 47.
    K. B. Lyons and P. A. Fleury, Solid State Comm. 23, 477, 1977.ADSCrossRefGoogle Scholar
  53. 48.
    E. Courtens, Phys. Rev. Lett. 37, 1581+, 1976.ADSCrossRefGoogle Scholar
  54. 49.
    P. A. Fleury and K. B. Lyons, Phys. Rev. Lett. 37, 1088, 1976.ADSCrossRefGoogle Scholar
  55. 50.
    See for example, “Anharmonic Lattices, Structural Transitions and Melting”, edited by T. Riste, Noordhoff, Leiden, 1974.Google Scholar
  56. 51.
    B. I. Halperin and C. M. Varma, P.R. B14, 4030, 1976.Google Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • P. A. Fleury
    • 1
  1. 1.Bell LaboratoriesMurray HillUSA

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