We examine the distinct part of the density autocorrelation function Fd(q,t), also called the intermediate scattering function, from the point of view of the vibration-transit (V-T) theory of monatomic liquid dynamics. A similar study has been report
ed for the self part, and we study the self and distinct parts separately because their damping processes are not simply related. We begin with the perfect vibrational system, which provides precise definitions of the liquid correlations, and provides the vibrational approximation Fdvib(q,t) at all q and t. Two independent liquid correlations are defined, motional and structural, and these are decorrelated sequentially, with a crossover time tc(q). This is done by two independent decorrelation processes: the first, vibrational dephasing, is naturally present in Fdvib(q,t) and operates to damp the motional correlation; the second, transit-induced decorrelation, is invoked to enhance the damping of motional correlation, and then to damp the structural correlation. A microscopic model is made for the transit drift, the averaged transit motion that damps motional correlation on 0 < t < tc(q). Following the previously developed self-decorrelation theory, a microscopic model is also made for the transit random walk, which damps the structural correlation on t > tc(q). The complete model incorporates a property common to both self and distinct decorrelation: simple exponential decay following a delay period, where the delay is tc(q, the time required for the random walk to emerge from the drift. Our final result is an accurate expression for Fd(q,t) for all q through the first peak in Sd(q). The theory is calibrated and tested using molecular dynamics (MD) calculations for liquid Na at 395K; however, the theory itself does not depend on MD, and we consider other means for calibrating it.
A new theoretical model for self dynamic response is developed using Vibration-Transit (V-T) theory, and is applied to liquid sodium at all wavevectors q from the hydrodynamic regime to the free particle limit. In this theory the zeroth-order Hamilto
nian describes the vibrational motion in a single random valley harmonically extended to infinity. This Hamiltonian is tractable, is evaluated a priori for monatomic liquids, and the same Hamiltonian (the same set of eigenvalues and eigenvectors) is used for equilibrium and nonequlibrium theory. Here, for the self intermediate scattering function Fself(q,t) we find the vibrational contribution is in near perfect agreement with molecular dynamics (MD) through short and intermediate times, at all q. This is direct confirmation that normal mode vibrational correlations are present in the motion of the liquid state. The primary transit effect is diffusive motion of the vibrational equilibrium positions, as the liquid transits rapidly among random valleys. This motion is modeled as a standard random walk, and the resulting theoretical Fself(q,t) is in excellent agreement with MD results at all q and t. In the limit for q to infinity, the theory automatically exhibits the correct approach to the free-particle limit. Also in the limit for q to zero, the hydrodynamic limit emerges as well. In contrast to the benchmark theories of generalized hydrodynamics and mode coupling, the present theory is near a priori, while achieving modestly better accuracy. Therefore, in our view, it constitutes an improvement over the traditional theories.
