IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v68y2014icp98-113.html
   My bibliography  Save this article

On the classical limit of quantum mechanics, fundamental graininess and chaos: Compatibility of chaos with the correspondence principle

Author

Listed:
  • Gomez, Ignacio
  • Castagnino, Mario

Abstract

The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess) to the correspondence principle. We will introduce a formalism for this classical limit that allows us to find the surfaces defined by the constants of the motion in phase space. Then in the integrable case we will find the classical trajectories, and in the non-integrable one the fact that regular initial cells become “amoeboid-like”. This deformations and their consequences can be considered as a threat to the correspondence principle unless we take into account the characteristic timescales of quantum chaos. Essentially we present an analysis of the problem similar to the one of Omnès (1994,1999), but with a simpler mathematical structure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:68:y:2014:i:c:p:98-113
    DOI: 10.1016/j.chaos.2014.07.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914001246
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.07.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. El Fakkousy, Idriss & Zouhairi, Bouchta & Benmalek, Mohammed & Kharbach, Jaouad & Rezzouk, Abdellah & Ouazzani-Jamil, Mohammed, 2022. "Classical and quantum integrability of the three-dimensional generalized trapped ion Hamiltonian," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Gomez, Ignacio S., 2018. "KS–entropy and logarithmic time scale in quantum mixing systems," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 317-322.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:68:y:2014:i:c:p:98-113. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.