What Are Coherent States and Their Relation to Perfect Solutions?

[impendingChaos]

I just watched the latest episode of NUMB3RS which brought up a very interesting concept called Coherent States. From what I got from the show this concept has something to do with data which contains no outliers and no anomalies, therefore pointing to a perfect solution. In the show it was stated that such a perfect set up is so improbable as to go against Coherent States.

I am just looking to see if the shows interpretation was correct and a simple explanation of what Coherent States are if they were not.

C.N.

 

[StatMechGuy]

I somehow think they totally missed the point. In quantum mechanics, coherent states (for the quantum harmonic oscillator, at least), provide position-momentum minimum uncertainty states. If you look at it in terms of second quantized electromagnetic fields, then they correspond to classical electromagnetic fields.

These states all correspond to "minimum uncertainty states" which kind of corresponds to what was on NUMB3RS.

 

[christianjb]

There could be several defn's of the term coherent state outside of QM. Wouldn't surprise me.

 

[reilly]

In QM, coherent states actually describe a Poisson Distribution, which allows for considerable variation, say, from the mean -- that is a coherent state can be quite variable.

I suspect that, who knows why, what they are talking about is a situation with perfect correlations, hence no unforseen variations. Never have heard of a coherent state in statistics. But...
Regards,
Reilly Atkinson

 

[Anonym]

Never have heard of a coherent state in statistics

Please, explain what you mean. For example, M@W and in particular Ch.12

Dany.

 

[reilly]

I base my comment on coherent States and statistics on 40 years of doing statistics. if there is such a thing as a coherent state in statistics then it is quite new -- perhaps connected with recent efforts with Robust
Statistics..

Regards,
Reilly Atkinson

What is M@W?

 

[Anonym]

M@W is abbreviation of L.Mandel and E.Wolf “Optical coherence and quantum optics”, Cambridge University Press, 1995. I am not sure, but I remember that you introduced that abbreviation few months ago.

“Size of photon particle”:

:” The bible on photon physics is Optical Coherence and Quantum Optics by Mandel and Wolf. It discusses, in great detail what I mentioned above. It assumes a sophisticated grasp of QM and statistics -- but it starts from ground zero, and does the basics -- state vectors, coherent fields, correlations,...-- albeit quickly. it is a great book, and it is worth the fight to read it.

I base my comment on coherent States and statistics on 40 years of doing statistics.

I use to ask questions if I have impression that I may study something new or the person will improve my understanding of the problem. By the way, my first post in PF addressed to you was about the coherent states.

In quantum mechanics, coherent states (for the quantum harmonic oscillator, at least), provide position-momentum minimum uncertainty states. If you look at it in terms of second quantized electromagnetic fields, then they correspond to classical electromagnetic fields.

Let check if we use the same notion. I mean a coherent state the solution of SE presented by E. Schrödinger, Die Naturwissenschaften, 14, 664, (1926). About 50 years ago the detailed investigation was initiated by R.J. Glauber et al. Specifically, I am interesting in the coherent states described by P. Carruthers and M. Nieto, Rev. Mod. Phys. 40, 411(1968) since they discuss the minimum uncertainty states which are not necessarily position-momentum and also the minimum uncertainty but not necessarily h/2. I agree that “the bible” is pretty accurate description of M@W.

Your statements:” Never have heard of a coherent state in statistics” and now:” if there is such a thing as a coherent state in statistics then it is quite new -- perhaps connected with recent efforts with Robust Statistics..” make me feel that I am reading a detective story. Besides the coherent states, what is wrong with Maxwell, Boltzmann, Gibbs, Einstein etc. which make it non robust?

Please start to tell the end and please include the relevant references.

Regards, Dany.

P.S. Sorry, it was Vanesch in “Particle-Wave duality and Hamilton-Jacobi equation”:
” But the q-variables in M&W are not exactly this.”

 

[Edgardo]

Here's something I found in the http://www.atsweb.neu.edu/math/cp/blog/?id=218&month=04&year=2007&date=2007-04-07 .
(Blog entry: Coherence, April 7, 2007)