On the theory of the superfluidity of two- and one-dimensional bose systems

A hydrodynamic Hamiltonian for two- and one-dimensional Bose systems is constructed by the method of functional integration. Its form indicates that there is superfluidity and two- fluid hydrodynamics at low temperatures despite the absence of a condensate. This result is clear from the fact that the single-particle Green's functions decrease at large distances in accordance with a power law in two-dimensional systems if $T\ne0$ and in one-dimensional systems if $T=0$, while they decrease exponentially in one-dimensional systems if $T\ne0$. A model is calculated for a two-dimensional low-density Bose gas; the thermodynamic functions and the equation of the phase transition curve are found. It is shown that allowance for quantum vortices in a two-dimensional Bose system does not alter the power-law decrease of the Green's functions at large distances.