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13
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84951211402
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F. Yonezawa, Y. Ishida, F. Martino, and S. Asano, in Liquid Metalsedited by R. Evans and D. A. Greenwood (Institute of Physics, London, 1977).
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(1976)
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18
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84951211403
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J.‐P. Hansen and I. R. McDonald, Theory of Simple Liquids2nd ed. (Academic, London) pp. 433–434.
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(1986)
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35
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85034892856
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T. L. Beck (private communication).
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46
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84951211401
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An overview of the simulation of collision‐induced spectra in condensed phases is given in Phenomena Induced by Intermodular Interactionsedited by G. Birnbaum (Plenum, New York).
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(1985)
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52
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84951211408
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G. Seeley and T. Keyes, J. Chem. Phys.91, (1989). 5581
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53
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85034899037
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There have been numerous treatments of phonons in disordered lattices using standard effective‐medium Green’s function techniques. There has also been extensive effort devoted to studies of phonons in models of network glasses. See, for example, Excitations in Disordered Systemsedited by M. F. Thorpe (Plenum, New York, 1982), and Structure and Excitations of Amorphous Solidsedited by G. Lucovsky and F. L. Galeener (American Institute of Physics, New York).
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(1976)
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54
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84983887516
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However, analogous theories that are capable of handling liquid‐like disorder—without restrictions to nearest neighbors or to Born models—are rather rare. Some recent progress in this direction has been made by H. Bottgér
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(1986)
Phys. Stat. Sol. B
, vol.138
, pp. 83
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Wegener, D.1
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55
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84951211390
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(though this paper makes no such claims). See also J. P. Stoessel and P. G. Wolynes, J. Chem. Phys.80, (1984), for a self‐consistent phonon theory in much the same spirit. 4502
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58
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84951211391
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order to make the presentation more transparent, we shall assume p orbitals on different atoms are orthogonal for the purposes of this paper. [There is a discussion of how nonorthogonality can be included within this approach in Ref. 2.] There is no equivalent assumption being made for phonons.
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60
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3843069055
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This analogy seems to strengthen the possibility that there is a specific relationship between our formalism and treatments of (dipole allowed) optical absorption which use Drude oscillator models:,;
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(1982)
Phys. Rev. Lett.
, vol.49
, pp. 1100
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Chandler, D.1
Schweizer, K.S.2
Wolynes, P.G.3
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66
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84951211392
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The primes represent derivatives with respect to r.
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73
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84951211393
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The [Formula Omitted] limit is trivial for this theory.
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75
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84951211394
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The MSA result is correctly normalized and positive‐definite, but it satisfies only the first (average value) moment condition exactly.
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76
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84951211395
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It would have been easy to obtain a more accurate hard‐sphere radial distribution function by using the modified hard‐core diameter prescribed by blip function theory (Ref. 43.), but there seemed little point in doing so here. Later in the section, when we make a comparison with simulation, we will use more accurate radial distribution functions.
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79
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84951211396
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N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia), p. 465.
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(1976)
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81
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84951211397
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The proof in frequency space is outlined by Geldard and Pratt (Ref. 23). The time‐domain result can be also shown directly by using the normal‐mode‐transformation matrix to prove a similar result for the position vectors, [Formula Omitted] and then relating a time derivative of the relevant position autocorrelation function to a velocity autocorrelation function.
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82
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0347007833
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These comparisons were performed at low temperatures where the effects of anharmonicity might not be expected to be all that pronounced. The nature of the anharmonicity of the liquid’s potential surface, and the evidence for it becoming more important as the temperature is increased, have been discussed in Refs. 11, 15, 16, 21, and 28, as well as by
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(1986)
J. Chem. Phys.
, vol.85
, pp. 6027
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LaViolette, R.A.1
Stillinger, F.H.2
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87
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84952278747
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Actual plots of the time correlation function predicted by Eq. (4.8) using the exact frequency spectrum of small Ar clusters show that [Formula Omitted] does indeed resemble the known velocity autocorrelation function until times of the order of [Formula Omitted](submitted).
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J. Chem. Phys.
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Adams, J.E.1
Stratt, R.M.2
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89
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84951211398
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The analogous idea for electronic bands would be to predict that the band edge predicted by some low level effective medium theory ought to correspond to the mobility edge for the electrons. This type of rough argument often works surprisingly well in the electronic problem. See, for example, Ref. 32.
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