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Towards a definition of the quantum ergodic hierarchy: Ergodicity and mixing

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  • Castagnino, Mario
  • Lombardi, Olimpia

Abstract

In a previous paper we have given a general framework for addressing the definition of quantum chaos by identifying the conditions that a quantum system must satisfy to lead to non-integrability in its classical limit. In this paper we will generalize those results, with the purpose of defining the two lower levels of the quantum ergodic hierarchy: ergodicity and mixing. We will also argue for the physical relevance of this approach by considering a particular example where our formalism has been successfully applied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:4:p:247-267
    DOI: 10.1016/j.physa.2008.10.019
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    References listed on IDEAS

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    1. Antoniou, I. & Suchanecki, Z. & Laura, R. & Tasaki, S., 1997. "Intrinsic irreversibility of quantum systems with diagonal singularity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 737-772.
    2. Castagnino, Mario & Lombardi, Olimpia, 2006. "The classical limit of non-integrable quantum systems, a route to quantum chaos," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 879-898.
    3. Castagnino, Mario, 2004. "The classical–statistical limit of quantum mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 511-517.
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    Cited by:

    1. Gomez, Ignacio S., 2018. "KS–entropy and logarithmic time scale in quantum mixing systems," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 317-322.

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