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The superfluidity mechanism of He II | J. X. Zheng-Johansson
; B. Johansson
; P-I. Johansson
; | Date: |
18 Jun 2002 | Journal: | in "New Developments in Superconductivity Research", R.W. Stevens Editor, The Nova Science Publishers, 2003. ISBN 1-59033-862-6 (augmented) | Subject: | cond-mat | Affiliation: | Bristol Univ., UK), B. Johansson (Uppsala Univ., SW), and P-I. Johansson (Uppsala Univ., SW | 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 $Kpropto$ $ 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 {f 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. | Source: | arXiv, cond-mat/0206339 | Services: | Forum | Review | PDF | Favorites |
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