Redfield equation implications

The Redfield equation describes the time evolution of the reduced density matrix of a system coupled to an equilibrium bath. The effect of the bath enters via the average coupling V = and the relaxation operator, the last sum on the right of Eq. (10.155). The physical implications of this term will be discussed below. 

Like the exact QDT counterpart [cf. Eq. (4.6)], the POP-CS-QDT preserves both the reduced Gaussian dynamics and the effective local field pictinre for the DBO system. Its TZg [Eq. (4.11a)] has the same dissipation superoperator terms as those in ]Zf [Eq. (4.6b)]. The first and the last terms in the right-hand-side of Eq. (4.11a) for TZg or Eq. (4.6b) for are mainly responsible for the energy renormalization (or self-energy) contribution [38] and their dynamics implications are often neglected in phenomenological quantum master equations such as the optical Bloch-Redfield theory [36]. Note that the bath response function relates to the spectral density as [cf. Eq. (2.8)]... 

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