# Steady state solution to density matrix

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.