Plots of the static structure factor (upper panel), Kubo transform of the intermediate scattering function (left panels), and the dynamic structure factor (right panels) for normal liquid helium at and . The solid lines are the results obtained from the NAC method and the open circles are the experimental results at from Ref. 83.
A plot of the frequency-dependent diffusion constant for normal liquid helium at and . The solid, dashed, dotted, and dot-dashed lines are the results from quantum mode-coupling theory (QMCT), numerical analytic continuation (NAC) method, Nakayama and Makri semiclassical (SC) approach (Ref. 32, ), and the centroid molecular-dynamics (CMD) simulation approach (Ref. 89), respectively.
A plot of the real part of the normalized velocity autocorrelation function for normal liquid helium and . The solid, dashed, and dotted lines are the results from QMCT, NAC method, and the Nakayama and Makri SC approach (Ref. 32, ), respectively.
Even time moments to fourth order of the velocity autocorrelation in atomic units. The PIMC result is the numerically exact result.
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