A second order optical process in a localized electron-phonon system is studied under a stationary excitation. A stochastic theory of vibrational relaxation at finite temperature is constructed based upon a quantum mechanical treatment. We project the dynamical motion of the whole lattice system onto the stochastic motion of a pseudo-local mode or a localized mode visualizing this mode as a damped harmonic oscillator which undergoes a Brownian motion. The overall emission spectrum is calculated and it is found that the relative intensities of the Raman scattering and luminescence components are determined competitively by two physical parameters, i.e., the radiative damping rate and the vibrational relaxation rate. It is also discussed how the relative orders of magnitude among various components of the secondary emission depend on the incident photon energy and the temperature of phonon system.
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