Three fluid hydrodynamics of superfluid3He

TheA₂-transition from theA₁ to theA-phase is the only known transition that seperates a state with a broken relative symmetry from one in which both constituent symmetries are independently broken. Therefore a question of interest here is what the Goldstone mode of this transition is. Employing two different points of view, one for its rigor and the other because of its plausible physical picture, a three fluid hydrodynamics is derived and employed to show that, with a grain of salt, theA₂-transition can be taken as marked by the onset of spin wave in a restricted geometry and by that of second sound generally. More quantitatively, the transition of the Goldstone modes takes place below theA₂ transitional temperature when the Leggett frequency is approached and is caused by two competing effects, hybridization and dispersion. In a fourth sound geometry these effects should be experimentally well accessible.