Crossover From One To Two Dimensions In Liquid He-4 In A Nanopore

Using diffusion and path-integral Monte Carlo methods, we show that liquid He-4 confined in a narrow nanopore of liquid radius R = 4 angstrom undergoes a crossover from a one-dimensional (1D) to a two-dimensional (2D) fluid as a function of liquid density. At low liquid density, e.g., a linear density rho(0) = 0.15 angstrom(-1), the liquid energy is at a minimum when the liquid lies in a line at the center of the pore. The pair distribution function g(x), the one-body density matrix n(x), and the superfluid fraction rho(S)/rho(0) all show 1D character that is well described by Luttinger liquid (LL) predictions. As density is increased, there is a crossover to 2D with the minimum energy configuration moving from a line at the center of the pore to a film near the pore walls. At linear density rho(0) > 0.40 angstrom(-1), the He-4 lies predominantly in a 2D cylindrical film midway between the center and the nanopore walls. The g(x), n(x), and rho(S)/rho(0) all show 2D character and the film has a low but finite transition temperature. He-4 at a bulk liquid density corresponds to rho(0) = 0.6 angstrom(-1) in the pore which lies in the 2D regime.