The density maximum of He4 at the lambda point modeled by the stochastic quantum hydrodynamic analogy

The lambda point in liquid He4 is a well established phenomenon acknowledged as an example of Bose-Einstain condensation. This is generally accepted, but there are serious discrepancies between the theory and experimental results, namely the lower value of the transition temperature Tl and the negative value of dTl /dP. These discrepancies can be explained in term of the quantum stochastic hydrodynamic analogy (QSHA). The QSHA shows that at the He4I\textregisteredHe4II superfluid transition the quantum coherence length lc becomes of order of the distance up to which the wave function of a couple of He4 atoms extends itself. In this case, the He42 state is quantum and the quantum pseudo-potential brings a repulsive interaction that leads to the negative dTl /dP behavior. This fact overcomes the difficulty to explain the phenomenon by introducing a Hamiltonian inter-atomic repulsive potential that would obstacle the gas-liquid transition.