Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: From Navier–Stokes-Like Equations to Landau-Like Criterion

Fractonic superfluids are exotic states of matter with spontaneously broken higher-rank $U(1)$ symmetry. The latter is associated conserved quantities that include not only particle number (i.e. charge) but also higher moments, such as dipoles, quadrupoles, and angular moments. Due to the presence quantities, mobility particles restricted either completely or partially. In this work, we systematically study hydrodynamical properties fractonic superfluids, especially focusing on constituent bosons called "lineons" $d$-components in $d$-dimensional space. From Euler-Lagrange equation, derive continuity equation Navier-Stokes-like equations, which moment conservation introduces extra terms. Furthermore, discuss current configurations related defects. Like conventional superfluid, critical values velocity fields density currents, gives rise a Landau-like criterion. At end several future directions discussed.