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The lambda point in liquid He4 is a well established phenomenon acknowledgedas an example of Bose-Einstain condensation. This is generally accepted, butthere are serious discrepancies between the theory and experimental results,namely the lower value of the transition temperature Tl and the negative valueof dTl /dP. These discrepancies can be explained in term of the quantumstochastic hydrodynamic analogy (QSHA). The QSHA shows that at theHe4I\textregisteredHe4II superfluid transition the quantum coherence length lcbecomes of order of the distance up to which the wave function of a couple ofHe4 atoms extends itself. In this case, the He42 state is quantum and thequantum pseudo-potential brings a repulsive interaction that leads to thenegative dTl /dP behavior. This fact overcomes the difficulty to explain thephenomenon by introducing a Hamiltonian inter-atomic repulsive potential thatwould obstacle the gas-liquid transition.

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