The superfluidity mechanism of He II

TL;DR

This paper proposes a quantum confinement effect (QCE) mechanism explaining superfluidity in He II, linking reduced phonon states due to confinement to superfluid behavior and critical velocity, aligning well with experimental data.

Contribution

It introduces the QCE superfluidity mechanism based on first principles, explaining superfluidity through quantum confinement effects on atomic states and phonon excitations.

Findings

Predicted viscosity matches experimental order of magnitude (<10^{-6})

Critical velocity $v_c(d)$ aligns with experimental data for channels >10^{-6} m

Discontinuities at energy gaps relate to superfluid critical velocities

Abstract

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.