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.

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user TanMath

Comments

The Lindblad equation is more or less as complicated as the Schrodinger equation. Is there a general solution to the Schrodinger equation?

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user DanielSank

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@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.

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user yuggib

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@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.

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user DanielSank

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@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.

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user yuggib

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@yuggib Oh you just mean $\exp[-i t H / \hbar]$?

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user DanielSank

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@DanielSank Yes, of course ;-)

This post imported from StackExchange Physics at 2015-08-16 03:57 (UTC), posted by SE-user yuggib