  Recent experiments on the flow of helium-4 fluid through nanopores with
tunable pore radius provide a platform for studying the quasi-one-dimensional
(quasi-1D) superfluid behaviors. In the extreme 1D limit, the helium atoms are
localized by disordered small variations in the substrate potential provided by
the pore walls. In the limit of wide pore radius, a solid layer of helium-4 is
expected to coat the pore walls smoothing out the substrate potential, and
superfluidity is observed in the central region. Building on earlier quantum
Monte Carlo results, we propose a scenario for this crossover using a shell
model of coupled Luttinger liquids. We find that a small radius pore will
always localize the helium atoms, but above a critical radius, a single 1D
channel flows through the pore and can be described by Luttinger liquid theory.

Mesoscale and Nanoscale Physics