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.

Automated summary

This study investigates the emergence of classicality from a stochastic quantum system through decoherence. The time-dependent parameters, such as mass, frequency, and damping coefficient, are considered. The invariant operator theory is used to describe the quantum evolution of the system, assuming equilibrium with the environment at a finite temperature. Decoherence characteristics, classical correlation, and quantum coherence length are analyzed. The decoherence time in both position and momentum spaces is estimated. The results show that the time dependence of the stochastic process affects the quantum-to-classical transition. The study is further applied to the damped harmonic oscillator, confirming the satisfaction of decoherence condition at high temperature, while classical correlation remains unaffected.