Simulation of dynamical properties of normal and superfluid helium

The formation of a superfluid when (4)He is cooled below the characteristic lambda transition temperature is accompanied by intricate quantum mechanical phenomena, including the emergence of a Bose condensate. A combination of path integral and semiclassical techniques is used to calculate the single-particle velocity autocorrelation function across the normal-to-superfluid transition. We find that the inclusion of particle exchange alters qualitatively the shape of the correlation function below the characteristic transition temperature but has no noticeable effect on the dynamics in the normal phase. The incoherent structure factor extracted from the velocity autocorrelation function is in very good agreement with neutron scattering data, reproducing the width, height, frequency shift, and asymmetry of the curves, as well as the observed increase in peak height characteristic of the superfluid phase. Our simulation demonstrates that the peak enhancement observed in the neutron scattering experiments below the transition temperature arises exclusively from particle exchange, illuminating the role of Bose-statistical effects on the dynamics of the quantum liquid.