TITLE: Uncertainty relations in the theory of open quantum systems

                   Department of Theoretical Physics,
                   Institute of Physics and Nuclear Engineering
                   Bucharest-Magurele, Romania

ABSTRACT:
 

In the framework of the Lindblad theory for open quantum systems we study the evolution of a particle moving in a harmonic oscillator potential and interacting with an environment at an arbitrary temperature. The Gaussian correlated coherent states, the squeezed states and Glauber coherent states are taken as initial states. We derive closed analytical expressions of the Heisenberg and Schr odinger generalized uncertainty functions of the damped harmonic oscillator for different regimes of time and temperature, in particular in the limiting cases of both zero and high temperatures of theenvironment and the limits of short and long times.

These expressions show explicitly how the quantum and thermal fluctuations contribute to the uncertainties in the canonical variables of the system.

In all considered cases the uncertainty relations are fulfilled, while in some other models considered in literature, the uncertainty relations are not fulfilled at someinitial moments of time.

We examine the relative importance of the quantum and thermal fluctuations in the evolution of the system from a quantum pure state to a non-equilibrium quantum statistical state and to an equilibrium quantum statistical state and analyze the relaxation process.

We find that the regime in which thermal fluctuations become comparable with the quantum fluctuations coincides with the regime in which the decoherence effects come into play, that is the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is comparable with the decoherence time calculated in similar models in the context of quantum to classical transitions.

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