Transverse sound in differentially moving superfluid helium

Abstract

There exists a transverse sound mode in superfluid helium, in addition to the first and second sound modes. In this mode, the velocity of the normal component oscillates in the direction perpendicular to the wave vector; hence, it is named the transverse mode. We analyze this mode at arbitrary values of the relative velocity of the normal and superfluid components. In general, temperature, pressure, and superfluid velocity also oscillate. The general relations between the amplitudes of the oscillating variables in the transverse mode are found in a general direction of the wave vector with respect to the relative velocity of the normal fluid and superfluid. We estimate the attenuation of the transverse mode in phonon pulses and discuss the possibility of detecting it experimentally.

Interactions of Phonons and Rotons with Interfaces in Superfluid Helium

“…In the current work we present the consistent solution of the problem of the interaction of quasiparticles with an interface for the case when their dispersion relation is arbitrary and non-monotonic, so that Ω 2 (k 2 ) is a polynomial of arbitrarily large degree S. The probability of the creation of each quasiparticle at the interface is derived for all cases. This work includes and generalizes the results of works [23]- [26], and in the special cases discussed previously, the expressions obtained here transform into the ones obtained earlier. So all results are now presented in a unified way.…”

“…Then in [26] the dispersion relation such that Ω 2 (k 2 ) is a cubic polynomial of k 2 was considered. It is the simplest expression that can approximate the distinctive dispersion relation of superfluid helium, in both the phonon and roton regions.…”

“…[3], were explained, and predictions were made for new experiments on the interaction of phonons and rotons with a solid. However, the use of a simple cubic approximation for the dispersion relation of superfluid helium restricted the results obtained in [26] to qualitative or semi-quantitative.…”

Second sound in an anisotropic quasiparticle system of superfluidH4e

“…The existence of the transverse mode, and the general relations between the amplitudes in this mode for arbitrary value of w, were established in Ref. 16, where we also discussed the possibility of experimentally detecting the transverse mode in phonon pulses in superfluid helium.…”

“…So, in superfluid helium there exists the mode = kv n which is the transverse mode. 16 To analyze the remaining four modes, which correspond to the first and second sounds, it is convenient to choose the coordinate frame with axis x directed along the equilibrium value of the relative velocity w, and axis y in the plane that is determined by vector w and wave vector k with the condition k y Ͼ 0 ͑see Fig. 1͒.…”