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Strong chaos in one-dimensional quantum system

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  • Yang, Ciann-Dong
  • Wei, Chia-Hung

Abstract

According to the Poincaré–Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie–Bohm’s trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E(∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position.

Suggested Citation

  • Yang, Ciann-Dong & Wei, Chia-Hung, 2008. "Strong chaos in one-dimensional quantum system," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 988-1001.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:4:p:988-1001
    DOI: 10.1016/j.chaos.2008.01.017
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    References listed on IDEAS

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    1. Yang, Ciann-Dong, 2006. "Modeling quantum harmonic oscillator in complex domain," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 342-362.
    2. Yang, Ciann-Dong & Wei, Chia-Hung, 2007. "Parameterization of all path integral trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 118-134.
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    Cited by:

    1. Yang, Ciann-Dong, 2009. "A new hydrodynamic formulation of complex-valued quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 453-468.
    2. Yang, Ciann-Dong, 2009. "Stability and quantization of complex-valued nonlinear quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 711-723.

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