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

Path integral centroid molecular dynamics (CMD) calculation for normal liqu id He-4 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 x 10(-5) cm(2)/s, which is in the same order of magnitude as t hat of ordinary liquids. Relaxation function of density fluctuation has als o been calculated within the CMD approximation. Detailed comparison between the static susceptibility function <(chi)over cap>(k) and the static struc ture factor of the centroid density (S) over cap((c))(k) has been made. The se correspond to the initial value of the exact and the centroid relaxation functions, respectively. For small k (less than or equal to 1.0 Angstrom(- 1)), <(chi)over cap>(k) is well approximated by (S) over cap((c))(k). For l arger k, both the correlation functions have identical peak position. Howev er, the intensity of (S) over cap((c))(k) is systematically larger than tha t of <(chi)over cap>(k). The calculated dynamic structure factor has been c ompared with the spectrum obtained from neutron scattering experiment. The agreement is satisfactory for 0.2<k<2.2 Angstrom(-1) . The calculated peak frequency as a function of k, i.e., the dispersion relation, has a minimum around 1.9 Angstrom(-1), where the static correlation function shows maximu m intensity. This behavior has also been experimentally observed for the di spersion relation for superfluid He-4. The peak continuously loses collecti ve character and shows single-particle behavior with increasing k around th e minimum. This behavior gives rise to the minimum in the dispersion relati on for normal liquid He-4. The spectrum becomes narrow as the peak approach es the minimum, showing that the single-particle contribution becomes domin ant in the dynamic structure factor. This narrowing is widely found among c lassical liquid; but is not observed in the spectrum of the superfluid He-4 , indicating that the excitation around the minimum for the superfluid may have a different molecular origin than that for normal liquid He-4. (C) 199 9 American Institute of Physics. [S0021-9606(99)50209-2].