The transient response of the second order optical process is studied for a localized electron-phonon system the stationary response of which was discussed in the preceding paper. We make use of the stochastic theory to project the dynamics of the whole lattice system onto the stochastic motion of the appropriately chosen relevant mode. The time-resolved emission spectrum is calculated for our model of vibrational relaxation which can be handled analytically. The time-dependent behaviors of various components of the secondary emission are clarified. The temporal characteristics of Raman (or Rayleigh) scattering components are determined by the phase memory time. On the other hand, the luminescence spectrum is composed of the ordinary and hot luminescence components. The characteristic time constant of the former is given by the radiative damping rate and that of the latter by the sum of the vibrational relaxation rate and the radiative damping rate.
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