Strong chaos in one-dimensional quantum system

Ciann-Dong Yang and Chia-Hung Wei

Chaos, Solitons & Fractals, 2008, vol. 37, issue 4, 988-1001

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:37:y:2008:i:4:p:988-1001

DOI: 10.1016/j.chaos.2008.01.017

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