Phonon excitations in 4He fluid film formed in 2.2Â nm diameter straight pores

We have measured the heat capacity of 4He adsorbed on straight one-dimensional (1D) pores 2.2 nm in diameter of the substrate FSM-16. Heat capacities of the 4He fluid film show the power laws close to T at low temperatures, and close to T2 at high temperatures around 0.5 K, suggesting a crossover from the low-temperature 1D state to the higher-temperature state. The results are well explained by assuming a phonon dispersion with continuous 1D states in the axial direction and discrete energy levels in the azimuthal direction.