I want to calculate the density matrix element's average over all the realization of Gaussian colored noise when the atomic system is coupled to the said noise. I know how to do it for atomic energy levels coupled to white Gaussian noise. The problem is with the Non-Markovian Gaussian colored noise. Can anyone tell me how to do this or can suggest some references? Do I need to use the stochastic Schrodinger equation or anything else? Do I need to use the Novikov theorem in order to calculate the noise average of the density matrix element as it is for white Gaussian noise, if yes how to calculate the functional derivative that will appear in the Novikov theorem?

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    $\begingroup$ How do you do it for white noise? It's really not that different for correlated noise... $\endgroup$ – DanielSank Jul 10 '19 at 18:29
  • $\begingroup$ For taking average over white noise the novikov theorem is required and it is straight forward to solve as white gaussian noise is Delta correlated..the problem comes when noise as finite correlation time... $\endgroup$ – Pradosh Jul 10 '19 at 18:35
  • $\begingroup$ While solving Novikov theorem for WGN we required to calculate functional derivative and this derivative is evaluated at t=t' as WGN is delta correlated...but for correlated noise it is not so straight forward....can you suggest some papers on this? $\endgroup$ – Pradosh Jul 10 '19 at 18:58

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