Time-Dependent Density-Functional Theory for Superfluids

A density-functional theory is established for inhomogeneous superfluids at finite temperature, subject to time-dependent external fields in isothermal conditions. After outlining parallelisms between a neutral superfluid and a charged superconductor, Hohenberg-Kohn-Sham-type theorems are proved for gauge-invariant densities and a set of Bogolubov-Popov equations including exchange and correlation is set up. Earlier results applying in the linear response regime are recovered.