Correlated driving and dissipation

The CODDE formulation of CS-QDT [Eqs. (2.21)] couples between p t) and a set of auxiliary operators K t) m > 0 that describe the effects of correlated driving and dissipation. The field-free dissipation action, TZs [Eq. (2.18)], can be evaluated relatively easily in terms of the causality spectral function Cab ( ) without going through the parameterization procedure of Eq. (2.24). The latter is required only for the correlated driving-dissipation effects described by the auxiliary operators. Methods of evaluating both the reduced dynamics p(t) and the reduced canonical density operator Peq(T) will be discussed in Sec. 3. 

The simplification arises also in evaluating the field-dressed part SQ t) [Eq. (B.3)] that determines the correlated driving and dissipation dynamics contribution Spt [cf. Eq. (2.17) or Eq. (B.4)]. In fact, 5Q t) in this case reduces to a c-number [38],... 

We now turn to the correlated driving and dissipation dynamics. The excitation field is chosen to be a transform-limited Gaussian pulse, e t) = cos(o ff), with the temporal center at t = 0 and the carrier frequency of cjf = Qh- The parameters for the pulse duration and the maximum strength are tc = lO/fin and respectively. 

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