Abstract
We studied the transport of $^{4}\mathrm{He}$ atoms through 2.5-mm-thick solid $^{4}\mathrm{He}$ samples sandwiched between two superfluid leads with five different tailor-made sample cells. Measurements in a cell with a barrier at the center of the solid samples and in a cell filled with silica aerogel establish the causal relation between the observed mass flow and the dislocation network in the solid sample. Comparing the results from these cells and prior measurements on solid samples with thicknesses of 2 cm and $8\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ reveals that the mass flow rate decreases logarithmically with the thickness of the solid $^{4}\mathrm{He}$. Interestingly, the mass flow exhibits both superfluid and bosonic Luttinger liquid characteristics at low temperature.
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