Finite-size Scaling of Four Helium Near the Superfluid Transition and Two-Dimensional Behavior of Three Helium in Four Helium Films

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Liquid helium displays a number of interesting properties at low temperatures. Some are unique to this quantum fluid, others are common to other systems, but observable with a higher degree of precision in helium. They have been studying critical behavior at the superfluid transition in the limit where helium is confined to such small dimensions that it no longer behaves as a three dimensional system. They have devised a technique for confining the helium between two well-spaced silicon wafers. They report first measurements of the superfluid density in which, as one approaches the superfluid transition, the helium deviates from three-dimensional behavior and then crosses over into two dimensions. They propose to continue these investigations for the next funding period as well as to start measurements of heat capacity. These data will provide stringent tests of finite-size scaling theories and dimensionality crossover. At low temperatures they have studied the superfluid transiton of near-monolayer films of 4He with 3He as an impurity. They report the observation that the transition of these films into the superfluid state takes place in two steps. They interpret this as a signature of the formation of the surface state for 3He. They propose to continue with these measurements to study other phenomena associated with the phase transition and the hydrodynamic mass of 3He.