NUMERICAL EVIDENCE FOR THE BOTTLENECK FREQUENCY OF QUASIDIFFUSIVE ACOUSTIC PHONONS

A kinetic equation on quasidiffusion of phonons was recently analyzed by Esipov and he predicted the existence of a bottleneck frequency (nu (BN)) which separates the phonons decaying from those diffusing to a d etector. We have solved numerically the kinetic equation and obtained the temporal evolution of phonon concentration excited at the center o f a spherical sample. We have also performed Monte Carlo simulations o f phonon propagation in the same geometry. At a time much later than t he ballistic arrival time of phonons, both sets of results exhibit a s harp peak in the phonon concentration around the predicted nu(BN) With Monte Carlo simulations we have also confirmed the same relaxation ra te for the phonons of frequencies nu>nu(BN).