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Quantum mechanics as a Markov process

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I am currently involved in some understanding on this matter with a colleague of mine. I know all the literature about but I do not know the state of art. Please, could you provide some relevant recent literature about? Also explanations are much appreciated.

My present view is that there exists a time scale that defines the limit of validity of a Chapman-Kolmogorov like equation. It is a situation very similar to quantum chaos but I do not know if this has been currently caught.

This post has been migrated from (A51.SE)
asked Nov 9, 2011 in Theoretical Physics by JonLester (376 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
There are some papers appeared in the '90s where the question was debated for the two-level model as http://pra.aps.org/abstract/PRA/v49/i3/p1607_1 that generated several comments and replies. But I think that the father of all these works is the one from Hanggi et al. http://pra.aps.org/abstract/PRA/v19/i6/p2440_1. What I need is a more up to date understanding of the situation. Yes, surely Nelson was one of the pioneers on this matter but I would like to know if it has been settled and, if yes, how.

This post has been migrated from (A51.SE)
Your Question at present brings to mind Edward Nelson's "Quantum Fluctuations", from 1985, Princeton University Press. That's usually taken to establish that QM is *non*-Markovian. Can you give some examples of the literature you mean?

This post has been migrated from (A51.SE)
Hmm, this could be an interesting question, but can you provide more background and expand the question a little bit?

This post has been migrated from (A51.SE)

1 Answer

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A short well-written starting point is Carlton Caves' on-line notes "Completely positive maps, positive maps, and the Lindblad form", see in particular Caves' discussion following (eq. 21), and the references provided.

It helps also to have a physical appreciation of "unravelling" as applied to quantum operations (the alternate spelling "unraveling" is common too); this term was (AFAICT) first introduced in Howard Carmichael's An Open Systems Approach to Quantum Optics (1993, see Section 7.4, p. 122).

In summary, a clear appreciation of the physical process of unravelling quantum trajectories, and the mathematical description of quantum trajectory unravelling as a Markov processes of Lindblad form, will go far to answer your questions.

No doubt other folks can recommend favorite references; please do so.

This post has been migrated from (A51.SE)
answered Nov 9, 2011 by John Sidles (485 points) [ no revision ]

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