Specific heat of liquid He-4 near the superfluid transition and confined in cylindrical channels

We present new measurements of the specific heat near the lambda transition of liquid He-4 at saturated vapor pressure and confined in micro-channel plates containing cylindrical holes. We investigated two channels diameters: 1$\mu$m and 2$\mu$m. Our results for the scaling function near the specific-heat maximum are in reasonably good agreement with previous measurements on channels with a 1 $\mu$m $\times$ 1 $\mu$m square cross section\footnote{M.O. Kimbal, K.P. Mooney, and F.M. Gasparini, Phys. Rev. Lett. {\bf 92}, 115301 (2004)} and on cylindrical channels with a 0.26$\mu$m diameter\footnote{J.A. Lipa, M. Coleman, and D.A. Stricker, J. Low Temp. Phys. {\bf 124}, 443 (2001)}. They also are consistent with the scaling function derived from Monte Carlo calculations.\footnote{N. Schultka and E. Manousakis, J. Low Temp. Phys. {\bf 111}, 783 (1998)} However, they suggest a size- dependent systematic departure from a unique scaling function that is consistent with earlier measurements$^3$ on cylindrical channels of 8$\mu$m diameter.