The point with zero momentum in the spectrum of acoustic phonon corresponds to a translation of the crystal.
Is there an interpretation like this of the Bogolyubov sound in BEC?
I have read that in BEC, the order parameter (a complex scalar) has a definite phase, which is a breaking of gauge symmetry. But I know little about gauge other than that in electromagnetism we can use different electromagnetic potential to obtain the same equation of motion.
Besides, I am unclear about the physical picture of BEC. Does the many-body wavefuction of the system in BEC have a definite phase?