Collective modes in superfluid helium when there is a relative velocity between the normal and superfluid components

Abstract

Collective modes are studied in superfluid helium when the normal and superfluid components have a relative velocity w. In this paper the general dispersion relation for first and second sound modes is obtained for arbitrary values of w, and we have found the relationship between the amplitudes of the oscillating variables for first sound. It is shown in a first sound wave, that both temperature and pressure can oscillate, and moreover, the normal fluid velocity can exceed the superfluid velocity in the wave. In the general case of first sound, the normal fluid not only has a velocity component parallel to the wave vector, but also a transverse velocity component. It is shown that when there is only a phonon system in the helium, the amplitude of the temperature oscillation in a first sound wave in an anisotropic phonon system, can exceed that in a second sound wave in an isotropic phonon system, for similar values of the normal fluid density.