Breakdown of detailed balance in current correlation functions and its implication on superfluid density

Detailed balance in current correlation functions, χ^<(ω) = e^-βωχ^>(ω), is the necessary condition for the fluctuation-dissipation theorem. Therefore, it is one of the most basic foundation for quantum theories of transport. Here, we find that the presence of superflow breaks this detailed balance such that the superfluid component is completely unaccounted for by the time-ordered current correlation function, χ(ω). This in turn leads to a convenient mean of evaluating superfluid density via the loss, χ^ret(ω=0) - χ(ω=0), against the retarded current correlation functions χ^ret(ω). This simple result offers a straightforward derivation of the standard world-line winding-number formulation, while avoiding several serious fundamental issues in the current derivations.