Determination of the Van Hove Spectrum of Liquid He(4):  An Application of the Feynman−Kleinert Linearized Path Integral Methodology

Abstract

The spectrum of the Van Hove correlation function (CF) is calculated for liquid He(4) at 27 K and a density of 0.25 g/cm3 by utilizing a recently proposed approximation to quantum CFs derived by combining an effective-frequency Boltzmann−Wigner transform with a linearized path integral expression for CFs. For this anharmonic system and highly nonlinear CF, we obtain excellent agreement with available accurate results. In particular, the first, second, and third moments of the spectrum are in very good agreement with both experiment and earlier theoretical results. Also, the calculated kinetic energy is in excellent agreement with accurate path integral Monte Carlo results.

Quantum diffusion in liquid water from ring polymer molecular dynamics

“…15͒ or larger than a factor of 2.0. 20 As has recently been shown in classical moleculardynamics simulations of TIP3P water, 49 and as we have confirmed here in the present simulations of the SPC/E model, there is also a significant additional increase in the selfdiffusion coefficient over that obtained in a small simulation when one extrapolates to the limit of an infinite system size ͑see Fig. 4͒.…”

“…[21][22][23][24][25] We have calculated orientational relaxation times and self-diffusion coefficients that are consistent with those found in a number of earlier approximate quantum-mechanical studies. [15][16][17][18][19][20] In addition, we have FIG. 4.…”

“…16 Several CMD studies of the orientational and translational motions in a rigid-body ͑TIP4P 2 ͒ water model have since appeared, 17,18 and two very recent studies have considered the dynamics of a flexible water model using the Feynman-Kleinert linearized path-integral ͑FK-LPI͒ approach. 19,20 The general conclusion of these papers is that quantummechanical fluctuations tend to increase the diffusion in the ambient liquid, the calculated increase in the self-diffusion coefficient over that obtained in a purely classical simulation varying from a factor of 1.4-2.0 depending on the interaction potential and the approximate quantum dynamical method employed. [15][16][17][18][19][20] This increase in the diffusion coefficient is consistent with the decrease in the structure of the liquid owing to quantum-mechanical effects that was observed in the earlier PIMC calculations.…”

“…19,20 The general conclusion of these papers is that quantummechanical fluctuations tend to increase the diffusion in the ambient liquid, the calculated increase in the self-diffusion coefficient over that obtained in a purely classical simulation varying from a factor of 1.4-2.0 depending on the interaction potential and the approximate quantum dynamical method employed. [15][16][17][18][19][20] This increase in the diffusion coefficient is consistent with the decrease in the structure of the liquid owing to quantum-mechanical effects that was observed in the earlier PIMC calculations. 13,14 Quantum-mechanical fluctuations evidently disrupt the hydrogen-bonding network in ambient water leading to a less structured liquid through which the water molecules diffuse more rapidly.…”

“…13,14 However, it is only comparatively recently that the role of quantummechanical effects in the dynamics of the liquid have been investigated. [15][16][17][18][19][20] The first people to consider these effects were Lobaugh and Voth, 15 who used the centroid molecular-dynamics ͑CMD͒ method to study the dynamics of a flexible simple point-charge ͑SPC/F͒ model of ambient water. This was followed shortly afterwards by a study in which the less sophisticated Feynman-Hibbs effective potential approach was used to calculate the self-diffusion coefficients of light and heavy water over a rather wide temperature range.…”