Lindblad equation solution

Question

I have been trying to solve a Lindblad Equation and then thought about whether there is a closed form Lindblad Equation solution for most types. Googling hasn't lead me to anything useful. So, is there some sort of generalized Lindblad Equation solution?

I am looking for something like the Schrondinger solution 
$U = exp(-i H t / hbar)$, but for Lindblad.

X.L.Li · Answer

We always solve the Lindblad form linear differential equations by numerical methods, such as fourth order Runge-Kutta method. If you want the steady state solution in analytic method, you can read this paper: PHYSICAL REVIEW A 92, 022116 (2015). I don't know if I solved your question.

Answered by X.L.Li on August 23, 2021

Nikodem · Answer

The analogy is based on writing the Lindblad equation in a Liouville form $dot{rho} = cal{L} rho$ with the Liouville superoperator
$cal{L}$ being the generator of the (semigroup) evolution for the density matrix $rho$.
The solution is then formally $rho(t) = e^{cal{L} t} rho(0)$.

Lindblad equation solution

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