Quasi-one-dimensional ${}^4\mathrm{He}$ inside carbon nanotubes

We report results of diffusion Monte Carlo calculations for both ${}^4\mathrm{He}$ absorbed in a narrow single walled carbon nanotube $(R=3.42\mathrm{}\AA )$ and strictly one-dimensional ${}^4\mathrm{He}.$ Inside the tube, the binding energy of liquid ${}^4\mathrm{He}$ is approximately three times larger than on planar graphite. At low linear densities, ${}^4\mathrm{He}$ in a nanotube is an experimental realization of a one-dimensional quantum fluid. However, when the density increases the structural and energetic properties of both systems differ. At high density, a quasicontinuous liquid-solid phase transition is observed in both cases.