In the scattering problem the zeros of the zeta function give the values of the momentum where the time delay changes strongly. The chaos of the Riemann zeta function is particularly apparent in a theorem that has only recently been proved: the zeta function fits locally any smooth function. The theorem suggests that the function may describe all the chaotic behavior a quantum system can exhibit. If the mathematics of quantum mechanics could be handled more skillfully, many examples of locally smooth, yet globally chaotic, phenomena might be found.

11 Comments

1. 1. archwayold 07:41 PM 10/27/08

   I long for the good old days when intelligent people dominated the news. The only way to get attention these days is to forecast doom or blow yourself up!

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2. 2. Itch 06:40 AM 10/28/08

   Am I being thick? The text refers to a number of crucial figures, where are they?

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3. 3. tonyv414 10:37 AM 10/28/08

   Tying this all to the zeta function seems to always be where such discussions of quantum (and other) chaos end. So many things seem to be built of characters which resemble the prime numbers - doesn't anyone notice the semantics of it all? When one asks the question " What exactly do I mean by prime and composite?" - one begins to realize that mathematics is "just another language".

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4. 4. gs_chandy 04:55 AM 10/29/08

   WHERE ARE THE FIGURES???

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5. 5. gmusser 05:15 PM 11/3/08

   Sorry about the lack of figures, folks. We didn't have them handy and thought it more important to get the article out than to wait for the images.

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6. 6. gs_chandy 09:46 PM 11/3/08

   The article is excellent. However, the lack of figures illustrating/discussing the text makes it much less valuable than it should be. Surely SciAm should have been able to get hold of those figures by now? Please do publish them and let us know that you have done so. Thanks, -- GSC

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7. 7. eco-steve 05:58 PM 11/26/08

   In arithmetic, operations are interchangeable if they are commutative. Nest non-commutative operations in program loops and results will be truncated with rounding errors, because decimal numbers are not reals. So such simple iterative loops cause results to go haywire within a few dozen repetitions. You can write computer programs to calculate as we do long-hand to great precision, but this increases execution times exponentially. No doubt to calculate quantum phases, computers are used, but how can we write programs which are not inherently chaotic, in view of the fact that we cannot know the position and velocity of a sub-atomic particle. Chaos theory applies to calculations as much as to physics. This article begs the question?

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8. 8. luzhiyang1118 01:18 AM 1/11/10

   It's excellent

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9. 9. BST 09:07 AM 4/29/10

   There are so many things to be understood from that text that I'm sure I don't understand the tenth of it.
   
   But quantum chaos seems to be a link between quamtum and classical mechanics. I am a determinist, I think that the probabilistic description of current quantum mechanics is just a statistical view of something that is in fact much more complex - a new mechanics to discover ? Anyway, I'm sure that quantum chaos has a role to play in all of this, I guess the future greatest progress in fundamental physics will have to do something with quantum chaos.

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10. 10. Eureka999 04:47 PM 6/27/10

    Consider the answer lays in the faqct that we need to look at the Universe at a much smaller scale.
    
    What if the electron itself was not a fundamental particle but made up from 1.23 x 10 to the power of 20, such particles. Now everything makes a lot more sense it is not a probability density distribution -it is a cloud. Moreover, a cloud is almost exactly what you see when you look at the electron experimentally and mathematically.
    
    You get quiter a lot of determinim back into your equations, but you haqve to remeber at that scale space-time is made nof the same harmonic quintessence. bottom mline is nyou will almost always get some chaos coming in - hence Heisenberg's uncertainty.
    
    The bonus is that you can now deirive things like E=mc2 from first principles. See: The formulation od harmonic quintessence and a fundamental enenrgy equivalence equation. See Physics Essays 23: 311-319.

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11. 11. rejumal 10:33 AM 10/7/10

    You can find the figures at http://www.dhushara.com/book/quantcos/qchao/quantc.htm I'm not sure why they haven't been included...?

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