Three-phonon interactions and initial stage of phonon pulse evolution in He II

Abstract

An expression for the characteristic rate of three-phonon processes in superfluid He4, which is valid in the entire range of phonon energies where three-phonon processes are allowed is derived proceeding from the hydrodynamic Landau Hamiltonian. Possible limiting cases are analyzed and compared with the results of previous investigations. It is found that three-phonon processes completely govern the initial relaxation of a phonon pulse injected into He II by a heated solid. As a result, the equilibrium form of phonon distribution is established in the anomalous region of phonon dispersion over a time interval of the order of 10−10 s.

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

“…Besides this the expression obtained in Ref. 18 for the rate of three-phonon processes is valid only in range 0 < < p p min . Here we shall carry out a detailed analysis of the rate of three-phonon processes in the range of momenta p p p min max < < in which the rate of three-phonon processes changes from the maximum value to zero.…”

“…Mathematically this fact is expressed by the appearance of h-functions which restrict the integration range. The rates represented in [18] do not contain these h functions. We note that these h functions cause the rapid decrease of the rates near the boundary momentum p max .…”

“…In Refs. 7,14-17, analytical relations for the boundaries of the areas and the expression (18) for the boundary momentum of phonon p¢ expressed by means of the function y and its first derivative were not obtained.…”

“…The rates of three phonon processes in isotropic phonon systems, at the saturated vapor pressure, were calculated in [18]. Experiments [4] were carried out at pressure of 0, 5, 12 and 18 , so in this work we investigate the rates at different pressures.…”

“…To calculate the typical rate of three-phonon processes in isotropic phonon systems, we follow [18], and substitute in the Eq. (30): n n n n n n n 1 10 2 20 3 30…”