How to determine the collapse operator for a Lindblad equation

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 $A$.

• Please define your terms "collapse" operator etc. very carefully in the post. This is a great question and deserves to be written well. – DanielSank Aug 5 '15 at 2:08
• @DanielSank I have edited it, is it better? – TanMath Aug 5 '15 at 2:18
• What environmental effect to do you want to model? This equation is somewhat general and can be applied to a variety of situations. – John M Aug 5 '15 at 3:01
• @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 – TanMath Aug 5 '15 at 22:22
• I don't think there's a simple procedure to do this. The collapse operator should be derived by considering the specific physical processes concerned. You could check Carmichael's book "statistical methods in quantum optics 1". – Pu Zhang Oct 10 '16 at 14:17