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

Abstract

The problem of the creation of high-energy phonons (h-phonons) by a pulse of low-energy phonons (l-phonons) moving from a heater to a detector in superfluid helium, is solved. The rate of h-phonon creation is obtained and it is shown that created h-phonons occupy a much smaller solid angle in momentum space, than the l-phonons. An analytical expression for the creation rate of h-phonon, along the symmetry axis of a pulse, are derived. It allows us to get useful approximate analytical expressions for the creation rate of h-phonons. The time dependences of the parameters which describe the l-phonon pulse are obtained. This shows that half of the initial energy of l-phonon pulse can be transferred into h-phonons. The results of the calculations are compared with experimental data and we show that this theory explains a number of experimental results. The value of the momentum, which separates the l- and h-phonon subsystems, is found.