Low-temperature Depletion of Superfluid Density in the Absence of Galilean Symmetry
Landau theory of superfluidity associates low-temperature flow of the normal component with the phonon wind. This picture does not apply to superfluids in which Galilean invariance is broken either by disorder, porous media, or lattice potential, and the phonon wind is no longer solely responsible for depletion of the superfluid component. Based on Popov's hydrodynamic action with anharmonic terms, we present a general theory for low-temperature ($T$) dependence of the superfluid stiffness, which reproduces Landau result as a special case when several parameters of the hydrodynamic action are fixed by Galilean invariance, and validate it with numerical simulations of interacting lattice bosons. In a broader context, our approach reveals universal low-temperature thermodynamics of superfluids with an intrinsic connection between finite-$T$ and finite-size ($L$) effects implying universal scaling, $T^{d+1}$ and $1/L^{d+1}$, respectively, for a large class of thermodynamic quantities. We discuss the experimental detection of this law, and compare our prediction to the existing literature.