Collective modes in the anisotropic unitary Fermi gas and the inclusion of a backflow term

We study the collective modes of the confined unitary Fermi gas under anisotropic harmonic confinement as a function of the number of atoms. We use the equations of extended superfluid hydrodynamics, which take into account a dispersive von Weizs\"acker-like term [C. F. von Weizs\"acker, Z. Phys. 96, 431 (1935)] in the equation of state. We also discuss the inclusion of a backflow term in the extended superfluid Lagrangian and the effects of this anomalous term on sound waves and the Beliaev damping of phonons [S. T. Beliaev, Sov. Phys. JETP 7, 299 (1958)].