Low-temperature Depletion of Superfluid Density in a Generic Superfluid: Not to Be Confused with the Phonon Wind

Landau's theory of superfluidity associating low-temperature flow of the normal component with the phonon wind does not apply to a generic case where Galilean invariance is fundamentally absent while the translation invariance takes place only at the level of the effective long-wave theory. In the generic case, the low-temperature phonon wind is an asymptotic metastable regime distinctively different from the depletion of the superfluid component. Based on Popov's hydrodynamic action, we present a universal theory of the low-temperature depletion of superfluid stiffness. Within this general framework, Landau's result corresponds to a special fine-tuning of parameters of the hydrodynamic action enforced by Galilean invariance. We illustrate our result with numeric simulations.