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, $\mathrm{\Delta }\mu$, and obeys $F\sim (\mathrm{\Delta }\mu {)}^b$, where $b\approx 0.3$ is independent of temperature. At fixed $\mathrm{\Delta }\mu$ the temperature dependence of the flux, $F$, can be adequately represented by $F \sim - \ln(T/\tau)$,$\tau \approx 0.6$K,for$0.1 \leq T \leq 0.5$ K. A single function $F=F_0(\mathrm{\Delta }\mu {)}^b\ln (T\mathrm{/}\tau )$ 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.