Critical point coupling in confined liquid helium-4 near the superfluid transition
Perron, Justin K.
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When two thermodynamic systems are in close proximity to each other some immediate questions arise such as "to what extent do the regions affect one another?" and "to what extent can these systems be considered isolated?" The answers to these questions are of course system dependent, however, for macroscopic quantum systems such as superconductors, superfluids and Bose Einstein Condensates, where the order parameter is a wave function, the answers have been provided by proximity effect theories. These theories predict that a system will only affect a neighboring system at a distance on the order of the correlation length ξ from the boundary. Reported here are measurements of the superfluid fraction ρ s /ρ, and the specific heat [special characters omitted] of arrays of (2μm) 3 boxes of liquid 4 He in equilibrium with ∼33 nm films. The spacing of the boxes in each array is varied for each measurement. The results are discussed in the light of proximity theories and indicate that for 4 He near the superfluid transition these theories fail to describe the observed effects since the effects of neighbouring regions are observable at distances much greater than ξ. These effects include enhancements in the specific heat of both the (2μm) 3 boxes and the connecting film, and enhancement in the superfluid density, as well as shifts in the temperatures of the superfluid onset and specific maximum. By quantifying these effects where possible, strong arguments are made indicating that, although spaced much farther than ξ, the correlation length is still the relevant parameter in these effects. This opens the door to questions involving ξ's physical interpretation. It is often thought of as the 'distance over which information is transferred'. If this is the case how can boxes spaced much larger than ξ 'know' of the neighbouring boxes? This remains an open question. Building on the evidence that the enhancements are related to the correlation length in the boxes, the data are used to map out the scaling locus of finite-size correlation length ξ( t , L ), where t = | T – T λ |/ T λ is the reduced temperature and L is the size of the confinement. This allows ξ( t , L ) to be calculated for our geometry and shows that at the bulk transition temperature ξ( t , L ) grows to only 14% of L.