Abstract
The velocity and attenuation of phonon second-sound waves in superfluid at saturated vapor pressure have been calculated, as a function of sound-wave frequency , over the entire frequency range at a single temperature 0.25°K. Second sound is obtained as a wavelike normal mode of a model phonon Boltzmann equation containing, in addition to the lifetime of a single thermal phonon due to small-angle scattering, a sequence of longer lifetimes characterizing wide-angle scattering of phonons with anomalous dispersion. The calculated second-sound phase velocity shows a dispersion spread out over four orders of magnitude in frequency in the range . Moreover, there is a wide frequency range satisfying in which a second-sound collective mode still propagates, with the same velocity as a thermal phonon but with an attenuation length much longer than the thermal-phonon mean free path. The existence of a collective mode in the regime , due to small-angle scattering, supports Maris's proposed explanation of resonancelike dispersion in the first-sound velocity, and also implies that the transition from collective to ballistic propagation in heat-pulse experiments is more complicated than previously supposed.
- Received 14 August 1975
DOI:https://doi.org/10.1103/PhysRevB.13.1105
©1976 American Physical Society