Interactions between Sheets of Phonons in LiquidHe4

Abstract

We have created two sheets of ∼1 K phonons in liquid 4 He at ∼55 mK such that they intersect each other as they move towards a common point. If the two sheets have a small angle between them, they interact strongly and create a hot line in the liquid helium. This line is continuously fed with energy from the two sheets and loses energy by creating high energy phonons. If the angle between the sheets is larger than ∼ 30 • they do not interact but pass through each other. These results give direct evidence for the composition of the sheets: they comprise strongly interacting low-energy phonons which occupy a narrow cone in momentum space.Phonon pulses have been created in cold liquid 4 He over many years since the initial work of Gernsey and Luszczynski in 1971 [1]. The pulses were found to travel at the velocity of sound and so it was believed, that to first order, the phonons were independent, non-interacting ballistic wave packets. The liquid 4 He was sufficiently cold that the ambient thermal phonons could be ignored. However it was recognised that phonons could spontaneously decay by the three phonon process (3pp) [2, 3], which is allowed by the upward curvature of the dispersion curve [4,5]. This picture was challenged recently by Adamenko et al. [6,7] who argued that a number of observations, such as the creation of high energy phonons in the liquid, could be explained if the phonons in the pulse were treated as strongly interacting and were confined to a narrow cone in momentum space. This has prompted us to look for evidence of the proposed phonon momentum distribution.A short electrical pulse in a planar thin-film heater is usually used to create a pulse of phonons. It was proposed [6,7], that the phonons in the 1

Three-phonon relaxation in isotropic and anisotropic phonon systems of liquid helium at different pressures

“…In a weakly anisotropic case the parameter c is close to unity. In our case, which corresponds to the experiments [4,5], the phonon pulses are strongly anisotropic phonon systems and c << 1.…”

“…10 as well as expression (5). It has long been realized that three-phonon processes cannot take place all the way to the critical momentum p c .…”

“…In experiments [4,5] the interaction of two phonon pulses was studied. In this connection the problem of calculating of the rate of their interaction is of undoubted interest.…”

“…The stimulus for carrying out this investigation were the experiments [4,5], where the interaction of phonon pulses was observed. These experiments have shown that pulses interact at pressures from 0 to 12 bar, and when the pressure is higher, for example, at 18 bar, there is no interaction.…”

“…The purpose of this paper is to calculate the rate of three-phonon processes in isotropic and anisotropic phonon systems of superfluid helium at different pressures and to compare the results of the calculations with experimental data [4,5].…”