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Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?

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  • Cafaro, C.
  • Ali, S.A.

Abstract

In this paper, we review our novel information-geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a simple application. Furthermore, knowing that integrable and chaotic quantum antiferromagnetic Ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies, respectively, we apply our IGAC to present an alternative characterization of such systems. Remarkably, we show that in the former case the IGE exhibits asymptotic logarithmic growth while in the latter case the IGE exhibits asymptotic linear growth.

Suggested Citation

  • Cafaro, C. & Ali, S.A., 2008. "Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6876-6894.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:27:p:6876-6894
    DOI: 10.1016/j.physa.2008.09.010
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    Cited by:

    1. Cafaro, Carlo & Mancini, Stefano, 2012. "On Grover’s search algorithm from a quantum information geometry viewpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1610-1625.
    2. Ali, S.A. & Cafaro, C. & Kim, D.-H. & Mancini, S., 2010. "The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3117-3127.
    3. Giffin, Adom & Cafaro, Carlo & Ali, Sean Alan, 2016. "Application of the maximum relative entropy method to the physics of ferromagnetic materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 11-26.

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