How to determine the collapse operator for a Lindblad equation

Question

Given a Hamiltonian $H$, how can I relate the collapse operator for the Lindblad equation to a given environmental effect? Also, how can I relate the constant $\gamma$ in front of the sum of the collapse operators to the full Hamiltonian?

For reference, the lindblad equation is:

$$\dot \rho = -i[H, \rho] + \left( \gamma \sum A \rho A^\dagger - \frac{1}{2} A^\dagger A \rho - \frac{1}{2} \rho A^\dagger A \right) \, .$$

When I say collapse operator, I am referring to the operator $A$.

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

Comments

Please define your terms "collapse" operator etc. very carefully in the post. This is a great question and deserves to be written well.

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

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@DanielSank I have edited it, is it better?

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

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What environmental effect to do you want to model? This equation is somewhat general and can be applied to a variety of situations.

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

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@JohnM pretty much any environmental effect.. But what I want is a procedure that I can use to find the collapse operator for this environmental effect to use in the Lindblad equation

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