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The heat capacity of pure ^3He in low density aerogel is measured at 22.5 bar. The superfluid response is simultaneously monitored with a torsional oscillator. A slightly rounded heat capacity peak, 65 mu K in width, is observed at the ^3He-aerogel superfluid transition, T_{ca}. Subtracting the bulk ^3He contribution, the heat capacity shows a Fermi-liquid form above T_{ca}. The heat capacity attributed to superfluid within the aerogel can be fit with a rounded BCS form, and accounts for 0.30 of the non-bulk fluid in the aerogel, indicating a substantial reduction in the superfluid order parameter consistent with earlier superfluid density measurements., Comment: 4 pages, 5 figures

Transition temperature data obtained as a function of particle density in the $^4$He-Vycor system are compared with recent theoretical calculations for 3D Bose condensed systems. In the low density dilute Bose gas regime we find, in agreement with theory, a positive shift in the transition temperature of the form $\Delta T/T_0 = \gamma(na^{3})^{1/3}$. At higher densities a maximum is found in the ratio of $T_c /T_0$ for a value of the interaction parameter, na$^3$, that is in agreement with path-integral Monte Carlo calculations., Comment: 4 pages, 3 figures

We have performed a high resolution specific heat measurement on 4He completely filling the pores of Vycor glass. Within 10mK of the superfluid transition we have found a peak in the heat capacity which is only 0.02% the size of the background. The peak can be fit with a rounded version of the ``logarithmic singularity'' observed in bulk 4He. Along with the previously observed ``2/3'' power law dependence of the superfluid density on temperature, this strongly suggests that the disorder imposed by the Vycor is irrelevant to the 3DXY superfluid phase transition. The critical amplitude of the peak, while in agreement with that found in other experiments in dilute superfluid 4He, is considerably larger than that predicted by the theory of hyperuniversality.

We have made simultaneous torsional oscillator and transverse NMR measurements (at 165 kHz) on 3He contained within aerogels with nominal densities of 1% and 2% of solid glass. The superfluid transition is seen simultaneously by both techniques and occurs at a temperature which agrees semi-quantitatively with that expected for homogeneous isotropic pair-breaking scattering of 3He atoms by strands of silica. Values obtained for the superfluid density rho_s in the 2% sample are in reasonable agreement with those observed previously. Coupling of the torsional mode to a parasitic resonance prevented accurate determination of rho_s for the 1% aerogel. We have identified other resonances coupling to the torsional oscillations as sound modes within the helium/aerogel medium., Comment: 17 pages, 10 figures

We have made simultaneous torsional oscillator and transverse cw NMR (at 165 kHz) studies of the superfluid phase of 3He in aerogel glasses of 1% and 2% of solid density. NMR occurs over a range of frequency extending from the Larmor frequency to higher values, but strongly peaked at the Larmor value. This behaviour together with the magnetic field independence of the effective superfluid density provides convincing evidence for a B-phase state with an n texture, in our spherical geometry, governed by the same energetic considerations as for bulk superfluid 3He-B., Comment: 4 pages, 3 figures, now contains changes made in response to referees' Comments and minor corrections

We have studied 4He films adsorbed in two porous glasses, aerogel and Vycor, using high precision torsional oscillator and DC calorimetry techniques. Our investigation focused on the onset of superfluidity at low temperatures as the 4He coverage is increased. Torsional oscillator measurements of the 4He-aerogel system were used to determine the superfluid density of films with transition temperatures as low as 20 mK. Heat capacity measurements of the 4He-Vycor system probed the excitation spectrum of both non-superfluid and superfluid films for temperatures down to 10 mK. Both sets of measurements suggest that the critical coverage for the onset of superfluidity corresponds to a mobility edge in the chemical potential, so that the onset transition is the bosonic analog of a superconductor-insulator transition. The superfluid density measurements, however, are not in agreement with the scaling theory of an onset transition from a gapless, Bose glass phase to a superfluid. The heat capacity measurements show that the non-superfluid phase is better characterized as an insulator with a gap., Comment: 15 pages (RevTex), 21 figures (postscript)