Abstract
The correlated projection superoperator techniques provide a better understanding about how correlations lead to strong non-Markovian effects in open quantum systems. Their superoperators are independent of initial state, which may not be suitable for some cases. To improve this, we develop another approach, that is extending the composite system before use the correlated projection superoperator techniques. Such an approach allows the choice of different superoperators for different initial states. We apply these techniques to a simple model to illustrate the general approach. The numerical simulations of the full Schrödinger equation of the model reveal the power and efficiency of the method.
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