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

Abstract

Starting from the kinetic equation for phonons in superfluid helium, expressions for the rates of three-phonon scattering in isotropic and anisotropic phonon systems were obtained for different pressures. These expressions are valid in the whole range of energies where three-phonon processes are allowed. Limiting cases were analysed and compared with the results of previous theoretical investigations. The obtained pressure and angular dependence of three phonon scattering rate allows one to explaine of the experimental data on interaction of phonon pulses.

Creation of high-energy phonons by four-phonon processes in anisotropic phonon systems of HeII

“…Then the rate rises monotonically with increasing q 1 and there is no range of angles where the rate decreases. This behavior is apparent whenp 1 13 ³ K, see Fig. 1,a.…”

“…, which correspond to the conditions of the experiments [13,14]. We see that there is a maximum whenp 1 13 < K. The appearance of this maximum atp 1 10 = K is caused by several reasons: firstly it follows from the conservation laws of energy and momentum that the four-phonon processes are prohibited if the angle between the momenta of phonons p 1 …”

“…Then the slow growth of the rate at these angles is determined by the factor R in the integrand of Eq. (38) and by the angular dependence of matrix element, see Fig 1, 1 and becomes greater than the angle q 1ME . Then the rate rises monotonically with increasing q 1 and there is no range of angles where the rate decreases.…”

“…The values of T p and q p can be estimated from the experimental data. However the description of the creation of h-phonons, at any angle to the anisotropy axis (see, for example, [1,2]), can only be made using the exact local-equilibrium distribution function (7) for the l-phonons. As that is the purpose of this paper, we shall use only the parameters c and T from now on.…”

“…On the time scale of the concerned problem, the equilibrium in the subsystem of l-phonons occurs instantly and the phonon distribution of this anisotropic phonon system is given by the Bose-Einstein distribution function with two parameters, temperature and drift velocity [1,2].…”