D Super Operator

From Qwiki

$\mathcal{D}$ (read "The Dee superoperator" ) is often refered to as the Decoherance superoperator or the Lindblad superoperator. The action of this operator on a state $ρ$ is

$\mathcal{D}[A]\rho = A\rho A^{\dagger} - \frac{1}{2}[A^{\dagger}A\rho+\rho A^{\dagger}A]$ .

The Lindblad superoperator describes the effect of coupling to a Markovian reservoir when only the system is to be modeled dynamically. While useful for modeling a range of decoherence phenomena, the superoperator can only be used when bath correlations can be neglected, i.e. bath correlations decay rapidly in comparison to system dynamics.