[en] We report measurements of the specific heat near the superfluid transition of ⁴He confined to 1 μm³ cylindrical boxes patterned in SiO₂. This system crosses from a 3D behavior to a 0D behavior near the transition. This has a marked effect on the specific heat as seen by a pronounced rounding of the maximum and a shift to a temperature much lower than the transition of the bulk system (and systems with 2D or 1D crossover). We plot the data according to correlation-length scaling theory and compare this to a planar system with the same smallest confinement. Compared to our previous studies of planar systems, the 0D cell has 3x the surface to volume ratio as well as ∼750x as much edge length. We examine the regions where surface and edge effect contributions can be separated. We find that the data do not reach the expected value for the surface region. There is also evidence for a region where the term associated with edge contributions dominates

[en] We have obtained the superfluid fraction of ⁴He and mixtures confined in channels 0.0185 μmx1.08 μmx∞. We compare this with film data Lx∞x∞, and data for channels 0.0483 μmx3.0 μmx∞. The behavior of the data in the smallest channels is quite different from what one might expect for a planar film of a given thickness. The transition is shifted to a lower temperature than expected; and, the overall behavior of ρ_s does not follow the trend observed with other confined films. This suggests that the lateral dimension plays a significant role in the behavior. We believe our observations are consistent with the recent proposal of Sobnack and Kusmartsev about a new mechanism for vortex unbinding in 2D films

[en] We report measurements of the superfluid fraction of 4He confined in small channels 9.4 nm high, 19 μm wide by 2000 μm long. This confinement corresponds to a film of finite lateral extent. The data show a shift in the transition to a lower temperature which is larger than the logarithmic dependence expected from finite-size scaling and Berezinski -Kosterlitz-Thouless theory. This shift however is smaller than the one proposed by Sobnack and Kusmartsev for this kind of geometry. When examining the behavior of the shift for confinement at several widths, we found that the shift favors a power law with a larger exponent than predicted by Sobnack and Kusmartsev