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Register a new userVibrational Contribution to Density and Current Autocorrelations in a Monatomic Liquid
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We consider for a monatomic liquid the density and current autocorrelation functions from the point of view of the Vibration-Transit (V-T) theory of liquid dynamics. We also consider their Fourier transforms, one of which is measured by X-ray and neutron scattering. In this description, the motion of atoms in the liquid is divided into vibrations in a single characteristic potential valley, called a random valley, and nearly-instantaneous transitions called transits between valleys. The theory proposes a Hamiltonian for the vibrational motion, to be corrected to take transits into account; this Hamiltonian is used to calculate the autocorrelation functions, giving what we call their vibrational contributions. We discuss the multimode expansions of the autocorrelation functions, which provide a physically helpful picture of the decay of fluctuations in terms of n-mode scattering processes; we also note that the calculation and Fourier transform of the multimode series are numerically problematic, as successive terms require larger sums and carry higher powers of the temperature, which is a concern for the liquid whose temperature is bounded from below by melt. We suggest that these problems are avoided by directly computing the autocorrelation functions, for which we provide straightforward formulas, and Fourier transforming them numerically.
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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 reported 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.
V-T theory is constructed in the many-body Hamiltonian formulation, and differs at the foundation from current liquid dynamics theories. In V-T theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion , and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na, and find the motion evolves in three successive time intervals: On the first vibrational interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second crossover interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third random walk interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. This motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.
In V-T theory the atomic motion is harmonic vibrations in a liquid-specific potential energy valley, plus transits, which move the system rapidly among the multitude of such valleys. In its first application to the self intermediate scattering function (SISF), V-T theory produced an accurate account of molecular dynamics (MD) data at all wave numbers q and time t. Recently, analysis of the mean square displacement (MSD) resolved a crossover behavior that was not observed in the SISF study. Our purpose here is to apply the more accurate MSD calibration to the SISF, and assess the results. We derive and discuss the theoretical equations for vibrational and transit contributions to the SISF. The time evolution is divided into three successive intervals: the vibrational interval when the vibrational contribution alone accurately accounts for the MD data; the crossover when the vibrational contribution saturates and the transit contribution becomes resolved; and the diffusive interval when the transit contribution alone accurately accounts for the MD data. The resulting theoretical error is extremely small at all q and t. Comparison of V-T and mode-coupling theories for the MSD and SISF reveals that, while their formulations differ substantially, their underlying atomic motions are in logical correspondence.
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