Mixture of Quantum States: Thermal and Interaction Inducing Decoherence

In this study, we show that the interaction energy plays an important role on the quantum decoherence: If we pay attention to the oscillation phase factor, $e^{-iE_{int}t/\hbar},$ we see that the time average of the macro-system's density matrix becomes nearly diagonal, where the states giving extrema of interaction energy are privileged to describe the quantum decoherence. This approach is compatible with the von Neumann's old work, which has been recently studied with renewed interest: The thermal mixture of states can be reached by the time average of a density of matrix due to the oscillation phase factor, $e^{-i(E_i-E_j)t/\hbar}.$ One of the direct results is the localization of macroscopic objects.