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In some references that I have read, a crucial assumption in deriving the Lindblad master equation is that the system and environment remain separable for all time. Hence, the system and environment cannot entangle with each other at any time. Hence, decoherence cannot occur.

However, there are papers which discuss decoherence dynamics using the Lindblad master equation. How can this be the case? An example of such a paper is "Decoherence by Lindblad Motion" by Klaus Dietz.

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  • $\begingroup$ Could you give an example of such a reference? $\endgroup$
    – alanf
    Commented Jul 1 at 5:56
  • $\begingroup$ The term 'separable' is usually applied to the Hilbert spaces of the system and environment. If the interaction Hamiltonian spans both, entanglement can occur. Is that the case here? $\endgroup$
    – Martin Vaughan
    Commented Jul 1 at 6:01
  • $\begingroup$ Separable here is used in the physicist sense. In other words, the composite state is assumed to be a product state $\lvert s \rangle \otimes \lvert e \rangle$ for all time. @MartinVaughan $\endgroup$
    – Silly Goose
    Commented Jul 1 at 6:05
  • $\begingroup$ I added one @alanf $\endgroup$
    – Silly Goose
    Commented Jul 1 at 6:09
  • $\begingroup$ I had a quick look at that reference. I could only find mention of a '... Hamiltonian with a separable (factorized)system–environment interaction ... '. Is there somewhere else where the actual system is asserted to be separable? $\endgroup$
    – Martin Vaughan
    Commented Jul 1 at 7:00

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The Born approximation is motivated by the idea that the environment is large compared to the system of interest and the interaction between the system and the environment is weak so that the environment's density operator remains unchanged to second order. See Section 3.2.3 of Maximilian Schlosshauer's review of decoherence:

https://arxiv.org/abs/1911.06282

For a discussion explaining why it is sometimes a good approximation to say the environment's state has not significantly changed even though the system has become entangled with it, see Chapter 11 of "Quantum Thermodynamics" by Gemmer, Michel and Mahler.

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