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Liquid 4He: Contributions to First Principles Theory. I. Quantized Vortices and Thermohydrodynamic Properties

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Quantized vortices in liquid 4 He are treated quantum mechanically with realistic many-body model wave functions in variational calculations for energy and core structure at T =  0 K. A rectilinear vortex and both small and large vortex rings are studied. Calculated results indicate that rotons are not just small-quantized vortex rings. We compare our results for quantized vortices with experimental data and with theoretical results calculated by others. Correlated basis functions and standard statistical mechanics are used in treating thermohydrodynamic properties of flowing liquid 4 He. The Helmholtz potential is evaluated for a model of the flowing liquid that includes phonons and interacting rotons. Characteristics of this potential are discussed. The physical nature of negative superfluid density is explained. Superfluid density, entropy, and specific heat for liquid He-II are evaluated using our theory and the results are compared with experimental data. Very good agreement is found, except in a small temperature range near the λ transition. We indicate that results obtained here can be used in extending the theory to include thermally excited vortices and to investigate the possible role of vortices in accounting for the λ transition in liquid 4 He.

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Jackson, H.W. Liquid 4He: Contributions to First Principles Theory. I. Quantized Vortices and Thermohydrodynamic Properties. J Low Temp Phys 146, 329–392 (2007). https://doi.org/10.1007/s10909-006-9252-2

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