Decoherence and Transition to Classicality for Time-Dependent Stochastic Quantum Systems with a General Environment.

The emergence of classicality from a stochastic quantum system through decoherence is investigated. We consider the case where the parameters, such as mass, frequency, and the damping coefficient, vary with time. The invariant operator theory is employed in order to describe quantum evolution of the system. It is supposed that the system is in equilibrium with the environment at a finite temperature. The characteristics of decoherence, the classical correlation and the quantum coherence length are analyzed. The decoherence time is estimated in both position and momentum spaces. We verify from such analyses that the time dependence of the stochastic process affects the quantum-to-classical transition of the system. To promote the understanding of the results, we apply our development to a particular system which is the damped harmonic oscillator. Through this application, we confirm that the decoherence condition is satisfied in the limit of a sufficiently high temperature, whereas the classical correlation is not affected by the temperature.