Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Quantum mechanics as a Markov process

+ 5 like - 0 dislike
1018 views

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 (345 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
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)
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)
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)

1 Answer

+ 6 like - 0 dislike

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 ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOve$\varnothing$flow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...