Echoes in glasses

We show that the time Tf for the exchange of energy between like defects in glasses is shorter (Tf~10^-8 sec) than a characteristic time T₁({~} 10^-4 sec) associated with direct relaxation of the defects to the "lattice" by one-phonon processes. This suggests that spin-spin flip processes constitute an important source of echo decay in glasses. We study the decay of the spontaneous echo amplitude, as a function of temperature and time separation between pulses, due to spin-spin flip processes in two different approximations. One of them takes into account explicitly correlation between flip-flop transitions. The shape of the echo-decay function and the order of magnitude of the phase memory time is obtained in both approximations. Finally we compare our results with recent experiments on phonon echo in glasses.