The density maximum in liquid He4 and its relationship to the lambda point

Zero point energy and the origin of the density maximum in water

“…In a recent communication [22] we showed that the existence of the density maximum in liquid He 4 could be explained in terms of this ZPE effect acting in opposition to the classical expansion/contraction. Specifically, as the temperature falls, more and more helium atoms drop into the ground state, causing the fluctuations in kinetic energy K to increase and hence the system to expand.…”

The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point

“…Recently, Deeney et al [8] showed that a quantum source of energy leading to the expansion of the condensate may explain the negative dT λ /dP behavior. The SQHA model supports this hypothesis showing that the quantum pseudo potential (QPP) (that acts only in the quantum condensed state) generate a repulsive force leading to the anomalous behavior at lambda point.…”

“…Moreover, given dT c /dP ~ d∆T c /dP it follows that dT c /dP ∝ a n 2 d(V −2 )/dP > 0 (8) since V decreases with the pressure. Feyman [4] in 1953 and later Butler and Friedman [5,6] calculated in detail the contribution of the inter-molecular potential for a bosonic system showing that it would need a repulsive potential, causing an expansion of the gas, in order to lower T B as one might expect from (7) (i.e., ∆T c < 0 ).…”

The internal energy and thermodynamic behaviour of a boson gas below the Bose–Einstein temperature

“…We have already commented upon this in a general way elsewhere [6]. There we noted that liquid 4 He is a particularly simple liquid, in that its atoms are spherically symmetrical and the interatomic forces are purely van der Waals' in nature.…”