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In the framework of the Lindblad theory for open quantum systems, we deriveclosed analytical expressions of the Heisenberg and Schr\"odinger generalizeduncertainty functions for a particle moving in a harmonic oscillator potential.The particle is initially in an arbitrary correlated coherent state, andinteracts with an environment at finite temperature. We describe how thequantum and thermal fluctuations contribute to the uncertainties in thecanonical variables of the system and analyze the relative importance of thesefluctuations in the evolution of the system. We show that upon contact with thebath the system evolves from a quantum-dominated to a thermal-dominated statein a time that is of the same order as the decoherence time calculated in othermodels in the context of transitions from quantum to classical physics.Comment: 23 pages, 8 figure

Uncertainty functions of the open quantum harmonic oscillator in the Lindblad theory