Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?
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4$\begingroup$ Chaos occurs in quantum physics and it does so in a very rich way. May I suggest a free web book "Classical and Quantum Chaos" by Cvitanović et al.. I've enjoyed it very much! $\endgroup$– Stipe GalićCommented Jan 18, 2013 at 18:35
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3$\begingroup$ Chaos applies to the mathematical formalism in many disciplines. en.wikipedia.org/wiki/Chaos_theory : "Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, engineering, economics, biology, and philosophy" $\endgroup$– anna vCommented Jan 18, 2013 at 18:39
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5$\begingroup$ Quantum chaos does not behave in exactly the same way as classical chaos, and does not formally satisfy all the definitions of a classical chaotic system. However, there is lots of material written about quantum chaos and it is an active area of study. $\endgroup$– Peter ShorCommented Jan 18, 2013 at 21:59
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2$\begingroup$ What is the difference between quantum chaos and ordinary ? Do not just quote wiki when you reply to that plz. $\endgroup$– mickCommented Jan 18, 2013 at 23:23
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$\begingroup$ General Relativity also has chaos, although it is harder to define corresponding terms with newtonian dynamics (lyapunov exponents) since GR formulation uses intrinsic geometry. See this paper: arxiv.org/abs/gr-qc/9602054 $\endgroup$– Benjamin HorowitzCommented Jan 18, 2013 at 23:45
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3 Answers
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In this PhD thesis (unfortunately in German :-/, a follow up paper can be found here), it is shown how for an action of a field theory containing even and Grassman fields, the renormalization group equation can be solved numerically (after expanding the action in derivatives and the fields). To investigate the corresponding renormalization group flow in the respective coupling space, analogous methods known to investigate trajectories in the phace space of a nonlinear dynamic system can be applied in this case too. A trajectory in this coupling space starting with certain inital values of the coupling constants at the high energy cutoff evolving in the course of renormalization time (which is related to the lenght or energy scale considered) can be considered as analogue to a trajectory in phase space, starting from an initial condition and evolving in the course of time.
As described in this paper, the coupling constants in a renormalizable field theory can not only flow to, bypass, spiral in/out or circle around isolated fixed points, but a chaotic behaviour of the renormalization group flow could occur too. This could have potential applications in different fields such as spin glasses, neural networks, or even string theory.
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Since time evolution is linear for a quantum system, this rules out classical chaos in terms of hypersensivity to initial conditions. The question of how quantum theory could explain classical chaos is adressed from the perspective of decoherence. This interesting document may be of some help: http://www.iqc.ca/publications/tutorials/chaos.pdf
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$\begingroup$ According to scielo.org.za/pdf/sajs/v104n5-6/a0610406.pdf linear systems can exhibit chaotic behaviour if they are infinite-dimensional, and even a 1D particle in a box is an infinite-dimensional system. $\endgroup$– YodoCommented Jun 28 at 18:02
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There is a SHM wave equation based on Schroedinger's equation and Maxwell's equation for an elliptical wave function which produces chaos (Langtons ant). I guess this answers the question about SHM and chaos.
