Classical Lorentz harmonic oscillator model of photo-phonon inteaction

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The reciprocal of the damping rate in the classical Lorentz harmonic oscillator model is equal to the phonon lifetime due to the concept of dephasing. Without damping, an oscillator would continue indefinitely, but the damping rate indicates how quickly the oscillation is interrupted. In quantum mechanics, states experience dephasing, leading to a loss of coherence characterized by a specific lifetime. This loss of coherence ultimately results in the cessation of the oscillator's motion. Thus, the relationship between damping and phonon lifetime is rooted in the dynamics of coherence loss.
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Why the reciprocal of the damping rate in this model equal to the phonon lifetime? Can somebody give me a detailed exaplanation.

Thanks.
 
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The answer is dephasing. If there were no damping, an oscillator would go on forever. The damping rate is a characteristic rate at which the oscillation gets interrupted. In the quantum world, quantum states slowly dephase and have a lifetime describing this loss of coherence. With loss of coherence comes the destruction of the interaction, e.g. the oscillator stops oscillating.
 

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