Abstract
We calculate properties of a model of $^{4}\mathrm{He}$ in Vycor using the path integral Monte Carlo method. We find that $^{4}\mathrm{He}$ forms a distinct layered structure with a highly localized first layer, a disordered second layer with some atoms delocalized and able to give rise to the observed superfluid response, and higher layers of nearly perfect crystals. The addition of a single $^{3}\mathrm{He}$ atom was enough to bring down the total superfluidity by blocking the exchange in the second layer. Our results are consistent with the persistent liquid-layer model to explain the observations. Such a model may be relevant to the experiments on bulk solid $^{4}\mathrm{He}$, if there is a fine network of grain boundaries in those systems.
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