We present a density functional for liquid He, properly accounting for the static response function and the phonon-roton dispersion in the uniform liquid. The functional is used to study both structural and dynamical properties of superIIIuid helium in various geometries. The equilibrium properties of the free surface, droplets, and films at zero temperature are calculated. Our predictions agree closely with the results of ab initio Monte Carlo calculations, when available. The introduction of a phenomenological velocity-dependent interaction, which accounts for back6ow effects, is discussed. The spectrum of the elementary excitations of the free surface and films is studied.

We study the phase separation of helium mixtures inside thin channels in contact with a bulk 'He bath at zero temperature.It is found that the substrate potential favors mixing near the walls. While in bulk, the transition takes place between a He-rich mixture with 6.6% of He and pure 'He; in thin channels, the He-rich phase is richer in He and the He-rich phase contains a nonzero fraction of 4He. We anticipate that both phases can be superfluid, so that the superAuid line is detached from the coexistence region. The behavior of helium mixtures in porous aerogel is discussed in relation to the present findings.A mixture of liquid 3He and 4He is a fascinating binary fluid in which superfluid transitions and phase separations can be studied in a variety of situations. Recent experiments by Chan and collaborators [1]on helium mixtures in porous aerogel have lead to surprising new features which are not well understood. In the case of aerogel with 0.98 porosity, it is suggested that the phase diagram of 3He-4He mixtures is modified with respect to the bulk one. A new phase diagram is proposed for this system, in which the coexistence region is detached from the superfluid transition line, giving rise to an intriguing 3He-rich superfluid mixture. Experimental evidence for this phase appears to persist down to zero temperature, with a 4He concentration as large as 20%. In contrast, 4He atoms are known to be completely excluded from bulk liquid 3He.There are two ways by which the aerogel may affect the helium phase diagram, namely disorder and confinement.Disorder is produced by the random interconnections of the delicate silica strands, about 30 A in diameter, constituting the gel, leaving open spaces of various size in which the liquid is confined In the p. resent Letter, we will not discuss the effect of disorder and focus our interest essentially on the effect of confinement on the phase separation at zero temperature. In this exploratory study, we use a simple geometry and consider helium mixtures inside thin channels of various size. In aerogel with 0.98 open volume fraction the size of the large pores are of the order of a few hundred angstroms. One thus expects in those pores a bulk behavior. Since we are interested mainly in the 3He-rich phases, there is no 4He in the bulk, so that the 3He chemical potential p, 3 is fixed to its bulk value, i.e. , -2.49 K. In other words-! and this is an essential aspect of the present workwe look for mixtures in thin channels in thermodynamical equilibirum with bulk 3He. Our main result is that both the size of the channel and the strength of the substrate potential drive the phase separation. The implications are twofold: (i) In contradiction to a common belief based on comparing the zero point motion of a 3He and a He atom, the liquid in the vicinity of the substrate is not pure 4He, but a 3He-He mixture with comparable concentrations of both isotopes. (ii) With decreasing channel thickness, the phase separation involves at the transition a He-rich phase which gets richer in...

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