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Mass flux characteristics in solid 4He for T> 100 mK: Evidence for Bosonic Luttinger Liquid behavior

At pressure $\sim$ 25.7 bar the flux, $F$, carried by solid \4he for $T >$ 100 mK depends on the net chemical potential difference between two reservoirs in series with the solid, $Δμ$, and obeys $F \sim (Δμ)^b$, where $b \approx 0.3$ is independent of temperature. At fixed $Δμ$ the temperature dependence of the flux, $F$, can be adequately represented by $F \sim - \ln(T/τ)$, $τ\approx 0.6$ K, for $0.1 \leq T \leq 0.5$ K. A single function $F = F_0(Δμ)^b\ln(T/τ)$ fits all of the available data sets in the range 25.6 - 25.8 bar reasonably well. We suggest that the mass flux in solid \4he for $T > 100$ mK may have a Luttinger liquid-like behavior in this bosonic system.