Theoretical Studies of Liquid He-4 Near the Superfluid Transition

We performed theoretical studies of liquid helium by applying state of the art simulation and finite-size scaling techniques. We calculated universal scaling functions for the specific heat and superfluid density for various confining geometries relevant for experiments such as the confined helium experiment and other ground based studies. We also studied microscopically how the substrate imposes a boundary condition on the superfluid order parameter as the superfluid film grows layer by layer. Using path-integral Monte Carlo, a quantum Monte Carlo simulation method, we investigated the rich phase diagram of helium monolayer, bilayer and multilayer on a substrate such as graphite. We find excellent agreement with the experimental results using no free parameters. Finally, we carried out preliminary calculations of transport coefficients such as the thermal conductivity for bulk or confined helium systems and of their scaling properties. All our studies provide theoretical support for various experimental studies in microgravity.