Refractive hydrodynamics of a quantum Bose fluid
Phys. Rev. B 113, 104510 – Published 13 March, 2026
DOI: https://doi.org/10.1103/v381-xypm
Abstract
We revise the quantum hydrodynamics of superfluids to account for the refraction of matter waves. Provided that the density fluctuations are small, the refraction may be incorporated into the low-energy theory by renormalization of the bare particle mass. We analytically demonstrate the consistency of the approach on a model system of hard spheres. At short wavelengths, the elementary excitation spectrum connects with the Beliaev expression featuring the roton minimum. Consecutive autolocalization of rotons and phonons at elevated densities results in a dramatic modification of the static structure factor as compared to the Bogoliubov theory: its shape approaches that characteristic of the random close packing. The isothermal compressibility diverges, signaling a first-order quantum phase transition. At moderate densities refraction stabilizes the Bose-Einstein condensate while reducing the superfluid fraction.
