Angular Momentum Correlation Function Research Articles

An effect of symmetry on the time dependence of correlation functions

In this work it is shown that because of the different symmetry of the variables the time dependence of the auto-correlation function of the time derivative of the anisotropic polarizability density can be different from that of the molecular angular momentum density auto-correlation function. Thus the information on this angular momentum correlation function that can be deduced from that of the time derivative of the anisotropic polarizability density can be limited.

Rotational Diffusion Model with a Variable Collision Distribution

Starting with an m-diffusion model a matrix description is given of the rotational motion of a dipole molecule undergoing frequent collisions. This treatment gives rise to an analytical expression for the dipole correlation function and for the angular momentum correlation function in which a limited number of parameters from the model appear. It is argued that the collision distribution which determines the rotational diffusion process need not necessarily be a Poisson distribution. In liquids with strong interactions the distribution is governed by the frequency distribution of the medium. This leads to the inclusion of a librational motion in the rotational diffusion model. A comparison of simulations with different collision distributions and experimental data is given.

Cooperative Phenomena and the Decay of the Angular Momentum Correlation Function at Long Times

A hydrodynamic solution for the decay of the angular momentum of an initially moving volume element in an otherwise stationary, compressible, viscous fluid predicts a long time decay of the angular momentum autocorrelation function which behaves as [ηst / Mρ]−(d+2)/2 where ηs is the shear viscosity, Mρ is the mass density, and d is the dimension of the system. This slow decay, which would not lead to the divergence of the rotational diffusion coefficient, or of the spin–rotation relaxation time, is caused by a vortex field which results from the interaction between a structured particle and host fluid. This result is analogous to the long time tail in the linear momentum autocorrelation function recently reported by Alder and Wainwright.

Time-Correlation Functions, Memory Functions, and Molecular Dynamics

The memory functions for the velocity, angular-momentum, and dipolar autocorrelation functions from a series of molecular-dynamics studies of liquid carbon monoxide are examined. The velocity and angular-momentum memory functions decay initially almost to zero in a Gaussian fashion. However, their long-time behavior has a much slower time dependence. The dipolar memory function from a simulation using a strong noncentral potential is approximately this system's angular-momentum autocorrelation function. Approximate velocity and angular-momentum correlation functions are generated from approximate memory functions and the results are compared to experiment. Gaussian memories based on the second and fourth moments of the corresponding autocorrelation functions give the best agreement with experiment. However, none of the approximate memories examined adequately represents the long-time behavior of the experimental memories. The static atomic radial distribution functions are given and are shown to depend upon the strength of the orientational parts of the pair potential used in the dynamics calculations. The non-Gaussian characteristics of the Van Hove self-correlation functions are examined and shown to depend on the potential and number of particles used in the dynamics calculations. The intermediate scattering function and its memory are also examined.

Application of the Statistical Model to Nuclear Magnetic Relaxation in Solid Hydrogen

The nuclear-spin relaxation of orthohydrogen molecules in solid ${\mathrm{H}}_{2}$ is due to the intramolecular dipole-dipole interaction modulated by the quadrupole-quadrupole interaction between $J=1$ molecules. Using the statistical method developed by Margenau and Anderson, we calculate the angular momentum correlation functions. In contrast to Moriya and Motizuki's result, where the Gaussian mode is used and relaxation times are found to be proportional to ${c}^{\frac{1}{2}}$ ($c$ is the concentration of orthohydrogen molecules in the solid), we obtain relaxation times proportional to ${c}^{\frac{5}{3}}$. Our result checks with the experimental data of Hardy and Gaines for $c<0.3$. In order to fit the experimental data for the entire range of concentration, a crystal field on the orthohydrogen molecules in the range 0.01-0.03\ifmmode^\circ\else\textdegree\fi{}K must be assumed.