The superfluidity mechanism of He II

Based on a first principles treatment of the excitation states we show that superfluidity of superfluid $^4$He (He II) results from a reduction in the number of phonon wavevector $K$ states $\N2(K)$ to a level that is negligibly low when the fluid is confined e.g. in a narrow channel, yet wider than the helium atom correlation length, $\Lambda$. This is as a result of the $K$ discretization, a manifestation of the quantum confinement effect (QCE). The predicted relative viscosity of a confined superfluid has the characteristic order of magnitude of experimental data ($<10^{-6}$). Furthermore, we show that at the edges of the resulting energy gaps, the $\N2(K)$ presents discontinuity. When its corresponding energy exceeds the (first) gap, the superfluid flow exhibits a critical velocity $v_c$. Our evaluation of $v_c(d)$ versus the channel width $d$, constrained to satisfy energy conservation, is in good quantitative agreement with experimental data for channels with $d>10^{-6}$ m. Meanwhile, a sharp turn about $K\propto$ $v_c$ in $\N2(K)$ resembles very well that of the experimental overshoot data. For narrower channels of $d<10^{-6}$ m $\le \Lambda$ in which the phonon excitation picture becomes inadequate, we instead represent the excitation in terms of single atoms with an effective mass, which yields a $v_c(d)$ in close agreement with experiment. Accordingly, the reduction in the number of atomic states results in superfluidity. The theoretical finding in this work, which can be termed the {\bf QCE superfluidity mechanism}, provides a consistent explanation for this puzzling phenomenon, the non-dissipative, superfluidity motion, of He II and could have a significant impact also on the understanding of other superfluids.