Superfluidity of classical liquid in a nanotube for even and odd numbers of neutrons in a molecule
This paper deals with mean-fields equations of the type \[ ih(\varphi '(x))_t=\left(-\frac{h^2}{2m}\Delta +W_t(x)\right)\varphi^t(x),\quad W_t(x)=U(x)+\int dyV(x,y)| \varphi ^t(y)| ^2, \] subject to the initial conditions \(\varphi (x,0)=\varphi_0(x)\), where \(\varphi_0\in W_2^\infty ({\mathbb R}^\nu )\). These equations arise in the study of various superfluidity phenomena occurring for classical liquids in nanotubes. The theory developed in the present paper establishes that the viscosity is connected with collisions of particles. In the case of a nanotube, the presence of the Bose condensate leads to the weakening of viscosity and consequently to superfluidity. The author also establishes that the major role in fermionic superfluidity is played by the attraction at long distances, while the repulsion at short distances is important for the appearance of bosonic superfluidity. In both cases, the transition to the condensate state (for pairs in the Fermi liquid) is a phase transition that has no relation to superfluidity. The proofs strongly rely on variational arguments combined with analytic tools.
scientific article; zbMATH DE number 5346138