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We present a path integral Monte Carlo study of the global superfluidfraction and local superfluid density in cylindrically-symmetric reservoirs ofliquid $^{4}$He separated by nanoaperture arrays. The superfluid response toboth translations along the axis of symmetry (longitudinal response) androtations about the cylinder axis (transverse response) are computed, togetherwith radial and axial density distributions that reveal the microscopicinhomogeneity arising from the combined effects of the confining externalpotential and the $^4$He-$^4$He interatomic potentials. We make a microscopicdetermination of the length-scale of decay of superfluidity at the radialboundaries of the system by analyzing the local superfluid density distributionto extract a displacement length that quantifies the superfluid massdisplacement away from the boundary. We find that the longitudinal superfluidresponse is reduced in reservoirs separated by a septum containing sufficientlysmall apertures compared to a cylinder with no intervening aperture array, forall temperatures below $T_{\lambda}$. For a single aperture in the septum, asignificant drop in the longitudinal superfluid response is seen when theaperture diameter is made smaller than twice the empiricaltemperature-dependent $^4$He healing length, consistent with the formation of aweak link between the reservoirs. Increasing the diameter of a single apertureor the number of apertures in the array results in an increase of thesuperfluid density toward the expected bulk value.

Path integral Monte Carlo simulation of global and local superfluidity in liquid $^{4}$He reservoirs separated by nanoscale apertures