Path-integral methods can be employed to calculate properties of boson systems at any temperature. We have performed a number of simulations of liquid helium and have calculated the momentum distribution as a function of temperature. We find that liquid helium has a condensate below 2 K but not above. The momentum distribution is found to be non-Gaussian even in normal liquid helium. We have also calculated the difference in the momentum distribution between a boson system and a distinguishable particle system.
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Ceperley et al. (1987) studied this question.