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KS–entropy and logarithmic time scale in quantum mixing systems

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  • Gomez, Ignacio S.

Abstract

We present a calculus of the Kolmogorov–Sinai entropy for quantum systems having a mixing quantum phase space. The method for this estimation is based on the following ingredients: i) the graininess of quantum phase space in virtue of the Uncertainty Principle, ii) a time rescaled KS–entropy that introduces the characteristic time scale as a parameter, and iii) a mixing condition at the (finite) characteristic time scale. The analogy between the structures of the mixing level of the ergodic hierarchy and of its quantum counterpart is shown. Moreover, the logarithmic time scale, characteristic of quantum chaotic systems, is obtained.

Suggested Citation

  • Gomez, Ignacio S., 2018. "KS–entropy and logarithmic time scale in quantum mixing systems," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 317-322.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:317-322
    DOI: 10.1016/j.chaos.2017.11.039
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    References listed on IDEAS

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    1. Gomez, Ignacio & Castagnino, Mario, 2014. "On the classical limit of quantum mechanics, fundamental graininess and chaos: Compatibility of chaos with the correspondence principle," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 98-113.
    2. Gomez, Ignacio & Castagnino, Mario, 2015. "A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 99-116.
    3. Gomez, Ignacio & Castagnino, Mario, 2014. "Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 112-131.
    4. Gomez, Ignacio S. & Portesi, M., 2017. "Gaussian ensembles distributions from mixing quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 437-448.
    5. Castagnino, Mario & Lombardi, Olimpia, 2009. "Towards a definition of the quantum ergodic hierarchy: Ergodicity and mixing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 247-267.
    6. Gomez, Ignacio S., 2017. "Lyapunov exponents and poles in a non Hermitian dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 155-161.
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