Quantum decoherence and classical correlation in quantum mechanics

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Abstract
We study two conditions for the quantum system to behave classically: decoherence in the quantum interference and the establishment of the classical trajectory in phase space. We show, despite the fact that these two conditions partially conflict with each other, the upside-down harmonic oscillator with a diffusion term satisfies them simultaneously. The implications for quantum cosmology and the measurement theory of quantum mechanics are given.