Dispersion Relation of Longitudinal Waves in Liquid He-4 in the Framework of Quantum Macroscopic Equations derived from Bohm's Potential

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 {\deg}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. Keywords: Bohm potential; Intermolecular potential; Dispersion relation; Superfluid He-4; First sound. PACS: 05.30.Jp; 05.20.Dd; 03.75.Kk; 67.25.dt