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New approach for deriving the exact time evolution of the density operator for a diffusive anharmonic oscillator and its Wigner distribution function

Using thermal entangled state representation, we solve the master equation of a diffusive anharmonic oscillator (AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation. We present a new evolution formula of the Wigner function (WF) for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space. It is found that this formula is very convenient in investigating the WF's evolution of any known initial state. As applications, this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.