Non-Hermitean transition operators

According to Eq. (10), the ACF of the non-Hermitean absorption transition moment operator of the high frequency mode is... 

Now, use the effective non-Hermitean Hamiltonians (228) to get the time dependence of the transition moment operator through Heisenberg transformation, but ignore non-Hermitean part for the Boltzmann operator. Then, the ACF taking into account both direct and indirect dampings, appears to be given by... 

As a consequence, it is possible to write the symmetrized Hermitean dipole moment operators in terms of symmetrized non-Hermitean absorption transition operators, according to... 

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