Current-density functional theory for bosonic superfluids

A finite-temperature current-density functional theory for bosonic superfluids (sf-CDFT) in the thermal equilibrium state is proposed herein. In the sf-CDFT, hydrodynamic physical quantities, such as particle number density, current density, and the order parameter of the Bose-Einstein condensation, are chosen as the basic variables. This theory enables the simultaneous reproduction of the particle number and current densities of both the superfluid and normal fluid components with incorporating effects of the interaction between these components. Specifically, these components are determined by solving two single-particle equations, i.e., the Gross-Pitaevskii-Kohn-Sham and Kohn-Sham equations. Furthermore, using the continuity equation of superfluids, we present the sum rule for the exchange-correlation energy functional of the sf-CDFT, which is useful for developing the approximate form.