Results for the Velocity Autocorrelation Function

Of all the time correlation functions, the velodty autocorrelation function has been studied most extensively. Of particular interest to us here is the work 

In Fig. 25 we give a rough sketch of the computer results for the dimensionless velocity autocorrelation function 

Finally, we mention the fact that the molecular dynamics calculation of Po t) for a gas of hard disks exhibited a vortex type of velocity correlation between the tagged molecule and the surrounding molecules that is very similar to the hydrodynamic flow field surrounding a moving volume element in a fluid initially at rest. This vortex pattern, illustrated in Fig. 26, suggests that a fraction of the momentum transferred by the tagged particle to the particles in front of it is eventually returned to it from behind. This process causes the velocity autocorrelation function to be larger than it would be if these vortices did not occur, and it is connected with the slow decay of the velocity autocorrelation function. 

Applications of the Kinetic Theory of Gases to the Time Correlation Fnnctions 

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 

---