Autocorrelation function short-time behavior

U. Buontempo, S. Cunsolo, and P. Dore. Intercollisional memory effects and short-time behavior of the velocity-autocorrelation function from translational spectra of liquid mixtures. Phys. Rev., A 10 913, 1974. 

Figure 1 a) The temporal profile of OHD-OKE on nitrobenzene. In the insert are shown the short-time behavior of the OKE transient solid line) and the intensity autocorrelation function of the laser pulse (dashed line) b) The light scattering spectrum of nitrobenzene measured by the double monochromator and the tandem interferometer (insert). 

FIGURE 4.11 Half-logarithmic representations of the field autocorrelation functions shown in Figure 4.10 to demonstrate that both short- and long-time behavior can be approximated by simple exponential functions (a) reduced graph to assess the short-time behavior (b) full graph to assess the long-time behavior. 

The kinetic theory of gases is, in principle, capable of determining the time dependence of po t) over all time intervals and for all densities of the gas. So far, however, only the short- and long-time behaviors have been studied in detail. Here we will concentrate on the long-time behavior of the velocity autocorrelation function, since it is of interest for the existence of the transport coefficients. " However, there is a large literature on the short-time... 

Mobility in this region is dominated by short-time motion, typically < 2 ps. After that time, all correlation of molecular motion is lost due to frequent collisions with the cavity walls. The center-of-mass velocity autocorrelation function of the penetrant exhibits typical liquid-like behavior with a negative region due to velocity reversal when the penetrant hits the cavity wall [59]. This picture has recently been confirmed by Pant and Boyd [62] who monitored reversals in the penetrant s travelling direction when it hits the cavity walls. The details of the velocity autocorrelation function are not very sensitive to the force-field parameters used. On the other hand, the orientational correlation function of diatomic penetrants showed residuals of a gas-like behavior. Reorientation of the molecular axis does not have the signature of rotational diffusion, but rather shows some amount of free rotation with rotational correlation times of the order of a few tenths of a picosecond, although dependent in value on the Lennard-Jones radii of the penetrant s atoms. 

An analysis of the intramolecular dynamics in terms of the Rouse modes yields non-exponentially decaying autocorrelation functions of the mode amphmdes. At very short times, a fast decay is found, which turns into a slower exponential decay which is well fitted by Ap exp(-f/Tp), see Fig. 13. Within the accuracy of these calculations, the correlation functions exhibit universal behavior. Zimm theory predicts the dependence Tp for the relaxation times on the mode number for polymers with excluded-volume interactions [6]. With v = 0.62, the exponent a for the polymer of length Am = 40 is found to be in excellent agreement with the theoretical prediction. The exponent for the polymers with Am = 20 is slightly larger. 

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