A finite one-dimensional microscopic model of a superfluid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal dissipationless motion of impurity with increased effective mass due to its interaction with the excitations of Bose fluid. It is shown that both the excitation spectrum of Bose fluid and the excitation spectrum of impurity can be analyzed using the structure of the ground state of the system.
The effective interaction energy of quasiparticles in the Bose fluid, which is described by ”ladder state diagrams” in the Bogoliubov approximation, was studied for a model potential. It is shown that in the Bogoliubov approximation, the interaction of excitations in liquid He can not be described even qualitatively. It means that a model of the weakly interacting dilute Bose gas fails in describing the interaction between excitation in Bose-condensed liquid, although this model qualitatively incorporates superfluidity in itself.