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The microscopic model of Ford, Kac, and Mazur for the interaction of an oscillator with a thermal reservoir is considered within the framework of stochastic quantization. The process executed by the Brownian particle is derived exactly and it is analyzed in detail. The phenomenological equations for the dynamics of the quantum oscillator in the equilibrium state, which we have previously derived, are recovered as the weak coupling limit of the exact theory.
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Ruggiero et al. (1983) studied this question.
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