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A density matrix follows the dynamics

$$ \dot{\rho} = \mathcal{L}\rho, $$

where $\mathcal{L}$ is the Liouvillian super-operator. If put in Lindblad form, it can be written as $$ \mathcal{L}\rho = -i[H,\rho] + A\rho A^\dagger - \frac{1}{2}\{A^\dagger A,\rho\}. $$ The steady-state of the system can be found by solving $\dot{\rho} = \mathcal{L}\rho = 0$. Under which circumstances is the solution unique? Thanks for the answer.

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