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Dispersion relation of longitudinal waves in liquid He-4 in the framework of quantum macroscopic equations derived from Bohm’s potential

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  • Molinari, Vincenzo
  • Mostacci, Domiziano

Abstract

He-4 is known to become superfluid at very low temperatures. This effect is now generally accepted to be connected with BEC (Bose–Einstein Condensation). The dispersion relation of pressure waves in superfluid He-4 has been determined at 1.1 °K by Yarnell et al., and exhibits a non monotonic behavior–with a maximum and a minimum–usually explained in terms of excitations called rotons, introduced by Landau. In the present work an attempt is made to describe the phenomenon within the Bohmian interpretation of QM. To this end, the effects of the intermolecular potential, taken to be essentially of the Lennard-Jones type modified to account for molecule finiteness, are included as a Vlasov-type self-consistent field. A dispersion relation is found, that is in quite good agreement with Yarnell’s curve.

Suggested Citation

  • Molinari, Vincenzo & Mostacci, Domiziano, 2015. "Dispersion relation of longitudinal waves in liquid He-4 in the framework of quantum macroscopic equations derived from Bohm’s potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 28-35.
    • Handle: RePEc:eee:phsmap:v:435:y:2015:i:c:p:28-35
    DOI: 10.1016/j.physa.2015.04.034
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    References listed on IDEAS

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    1. D. Mostacci & V. Molinari & M. Premuda, 2009. "A transport theory approach to percolation of liquids through porous media," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 127-132, July.
    2. Mostacci, D. & Molinari, V. & Pizzio, F., 2008. "Quantum macroscopic equations from Bohm potential and propagation of waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6771-6777.
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