Re: [Phys-l] Complementary principle in jeopardy?

[John Denker <jsd@av8n.com>]

On 06/15/2011 11:59 AM, curtis osterhoudt wrote:
> John, the "argument from authority" was a reference to a work on just
> the topic which was under discussion. Calling it an argument from
> authority is disingenuous at best. You made some heuristic arguments
> based on an ensemble, which is fine, but to which the strict
> definitions of adiabatic invariance probably don't apply. Arnold
> (authority? If so, too bad) specifically states that the in-phase
> driving situation is NOT one which Liouville's Theorem applies to, as
> do several other works on the subject.

If Arnold says that, Arnold is wrong.  So are a lot of other people.
I don't think I'm being coy or disingenuous when I say that.  I
really don't know how to say it any more more candidly or frankly
or bluntly.  That's the opposite of disingenuous.

As for heuristics, if you want the non-heuristic version, in gory 
detail, please refer to Phys. Rev. A _29_, 1419–1437 (1984).
   http://pra.aps.org/abstract/PRA/v29/i3/p1419_1
I cite that not because it authoritative, but because it is right.
The experiment has been done.

If you read that -- or if you just do the experiment -- you will 
find that the diagram I presented in this forum a few days ago 
  http://www.av8n.com/physics/img48/phase-space-sho.png
is quantitatively correct.  A certain type of area in phase space 
is invariant in this case, even though we are doing phase-locked 
pumping.  E/ω is not invariant in this case.  Liouville's theorem
is upheld.

> to which the strict
> definitions of adiabatic invariance probably don't apply.

Why do you say "probably"?  If you don't know whether or not the 
definitions apply, maybe you shouldn't be so opinionated about 
the subject.

In fact there is a vast literature on the subject of degenerate
parametric amplifiers.  I guarantee you, if Liouville's theorem
did not apply, it would have been noticed before now.
  http://scholar.google.com/scholar?q=%22degenerate+parametric+amplifier%22
  http://scholar.google.com/scholar?q=%22degenerate+parametric+amplifier%22+bogoliubov

Credit: Almost all of what I know about this I learned from Bernie
Yurke.  He seems to think I made some useful contributions, but he 
was definitely the brains of the operation.