E. L. Pollock

The normal and superfluid densities are defined by the response of a liquid to sample boundary motion. The free-energy change due to uniform boundary motion can be calculated by path-integral methods from the distribution of the winding number of the paths around a periodic cell. This provides a conceptually and computationally simple way of calculating the superfluid density for any Bose system. The linear-response formulation relates the superfluid density to the momentum-density correlation function, which has a short-ranged part related to the normal density and, in the case of a superfluid, a long-ranged part whose strength is proportional to the superfluid density. These facts are discussed in the context of path-integral computations and demonstrated for liquid $^{4}\mathrm{He}$ along the saturated vapor-pressure curve. Below the experimental superfluid transition temperature the computed superfluid fractions agree with the experimental values to within the statistical uncertainties of a few percent in the computations. The computed transition is broadened by finite-sample-size effects.

Computational techniques allowing path-integral calculations of quantum many-body systems are introduced and applied to liquid and solid helium. The computations presented in this paper do not include exchange effects. The range and limitations of the method are demonstrated by presenting thermodynamic properties, radial distribution functions, and, for the solid phase, the single-particle distribution and intermediate scattering function for imaginary times.

Discretized path-integral computations of the energy and radial distribution function of $^{4}\mathrm{He}$ in good accord with experiment are presented for temperatures down to 1 K at saturated vapor pressure. Results for the single-particle density matrix, momentum distribution, and condensate fraction agree at the lowest temperature with previous ground-state calculations.