An Exactly Solvable Superfluidity Model and the Phase Transition of the Zeroth Kind (Fountain Effect)

We present an exactly solvable $N$-particle Schrëdinger equation model for symmetric states (bosons), define a phase transition from the metastable (superfluid) state to the normal state for the model, and show that this is a phase transition of the zeroth kind with a free-energy jump and with specific heat tending to infinity. We also show that the asymptotic expression as $N\to\infty$ for the solution corresponding to the local Gibbs distributions coincides with the solution of the Hartree temperature equation, which illustrates our formula for the dependence of the Landau criterion on temperature in Bogoliubov"s almost-ideal Bose gas model.