Excitations of Neutral Superfluids and their Interactions

Question

I need some clarifications about the low energy excitations superfluids and their interactions.

First case, Bose superfluid: As far as I know, there are 3 kinds of commonly known excitations in this system:

1- Bogoliubov quasi particles

2- Higgs mode, or the amplitude mode of superfluid wave function, these are massive

3- Goldstone modes, or fluctuations of the phase of superfluid wave function, these are clearly massless

For a Bosonic superfluid, Bogoloibuv quasi particles are massless with dispersion

$$E(p)=\sqrt{c^2p^2+\frac{p^4}{4m^2}}$$ So we may say that quasi particles are not independent of Goldstone modes. And their interaction can be described by the Ginzburg Landau type functional.

Question 1: Is the above statement correct? Can the low energy physics be described entirely in terms of amplitude and phase modes using the quantum action? If the answer is yes, then how are the ladder operators for quasi particles are (heuristically) related to phase and amplitude operators? If the answer is no, then how can we describe the interaction between quasi particles and other excitation? For example, how can we find the decay rate of quasi particles due to their interaction with Goldstone modes?

Second case, Fermionic superfluid: If we assume the pairing between fermions to be s-wave (theoretically, I am not talking about real life superfluid Helium-3) then again we have massive amplitude modes and massless Goldstone modes. But Bogoliubov quasi particles are gapped in this case.

Question2: The same as question 1 for a Fermionic superfluid.

Answer 1

For a Bose superfluid the similarity to the relativistic Higgs potential is misleading. For such a fluid there are no separate gapped radial amplitude modes and gapless Goldstone modes. The Bogoliubov quasiparticles are phonons i.e quanta of sound waves, and sound involves both a change of density (radial) and longitudinal velocity (gradient of the order parameter phase).