One-Dimensional Second Sound in Superfluid Helium

Abstract

In the low temperature, phonon dominated, regime the velocity of second sound in superfluid helium approaches ${c_0}/\sqrt {3}$, where c ₀ is the ordinary acoustic sound velocity. Observation of this limiting behavior is difficult owing to the rapid decrease of the wide-angle scattering rate τ ⁻¹_⊥ as the temperature is reduced. At a given frequency ω, the product ωτ _⊥ soon exceeds unity and the mode collapses. Although wide-angle phonon scattering is required for the propagation of second sound, at low pressures and temperatures it is the nearly collinear (~5°) 3-phonon process that dominates the mean free path[l]. This is due to the phonon dispersion being anomalous or “upward” at small wavevector. Maris[2] showed that for times intermediate between τ _‖, the small-angle time and τ _⊥ a pseudo-temperature can be assigned to groups of phonons propagating in a given direction and equilibrating amongst themselves via the 3-phonon process. He further predicted that a new type of second sound would propagate in this one-dimensional regime with velocity close to c₀. It is the study of this new mode that we report on here.