A path integral centroid molecular dynamics study of nonsuperfluid liquid helium-4

Abstract

Path integral centroid molecular dynamics (CMD) calculation for normal liquid 4He has been performed. Dynamical behavior of the liquid at 4 K, which can not be reproduced by classical approximation, was well described by the CMD formalism. The calculated self-diffusion coefficient was found to be 5.06±0.04×10−5 cm2/s, which is in the same order of magnitude as that of ordinary liquids. Relaxation function of density fluctuation has also been calculated within the CMD approximation. Detailed comparison between the static susceptibility function χ̂(k) and the static structure factor of the centroid density Ŝ(c)(k) has been made. These correspond to the initial value of the exact and the centroid relaxation functions, respectively. For small k (⩽1.0 Å−1), χ̂(k) is well approximated by Ŝ(c)(k). For larger k, both the correlation functions have identical peak position. However, the intensity of Ŝ(c)(k) is systematically larger than that of χ̂(k). The calculated dynamic structure factor has been compared with the spectrum obtained from neutron scattering experiment. The agreement is satisfactory for 0.2<k<2.2 Å−1. The calculated peak frequency as a function of k, i.e., the dispersion relation, has a minimum around 1.9 Å−1, where the static correlation function shows maximum intensity. This behavior has also been experimentally observed for the dispersion relation for superfluid 4He. The peak continuously loses collective character and shows single-particle behavior with increasing k around the minimum. This behavior gives rise to the minimum in the dispersion relation for normal liquid 4He. The spectrum becomes narrow as the peak approaches the minimum, showing that the single-particle contribution becomes dominant in the dynamic structure factor. This narrowing is widely found among classical liquid; but is not observed in the spectrum of the superfluid 4He, indicating that the excitation around the minimum for the superfluid may have a different molecular origin than that for normal liquid 4He.