Choas and the bridge from Classical to Quantum physics

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Has there been work done exploring the possible connection between chaotic systems and quantum mechanics?

Chaos basically tells us that an infinitesimal change in initial conditions, given enough time, will lead to complete different solutions - another way of stating that is over enough periods, two different initial conditions will lead to completely different behavior.

That is, that there is inherent uncertainty in the behavior of chaotic systems, because it is impossible to ever know the initial state of the system to an infinitesimal degree of precision. Does anyone else see the similarity to quantum mechanics in that statement?

On the atomic scale, systems oscillate at extremely high frequencies, generally on the order of a GHz or more. I don't think it's a huge stretch to at least propose that perhaps there is some sort of chaos inherent in these systems (after all, most D.E.'s in quantum mechanics are non-linear), and maybe that is the fundamental reason we have to treat QM statistically, rather than deterministically.

Is this a whacked out idea?
 

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atyy
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http://chaosbook.org/

"Quantum chaos" is discussed in the latter part of the book.
Thanks! I read around a bit and found the book to be very interesting. By the way, is it me or does the author have a really good way with words and vocabulary (first few pages he uses a lot of nice ol vocabulary)? It looks effortlessly coherent.
 

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