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.

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    $\begingroup$ The Lindblad equation is more or less as complicated as the Schrodinger equation. Is there a general solution to the Schrodinger equation? $\endgroup$ – DanielSank Aug 6 '15 at 4:50
  • $\begingroup$ @DanielSank Yes there is a general solution to the Schrödinger equation; and also to the Lindblad equation, even if they are a little bit different. $\endgroup$ – yuggib Aug 6 '15 at 5:28
  • $\begingroup$ @yuggib well, if you mean a general solution in terms of eigenstates, then yes, I agree. It's really not clear to me what TanMath wants. I hope he/she will edit the question to make it more specific and clear. $\endgroup$ – DanielSank Aug 6 '15 at 5:36
  • $\begingroup$ @DanielSank For the Schrödinger equation, I mean a general solution as an evolution equation on Hilbert spaces; for the Lindblad equation as a semigroup equation on Banach spaces. I will make an answer to clarify. $\endgroup$ – yuggib Aug 6 '15 at 5:39
  • $\begingroup$ @yuggib Oh you just mean $\exp[-i t H / \hbar]$? $\endgroup$ – DanielSank Aug 6 '15 at 5:47

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.


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