IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v117y2018icp276-282.html
   My bibliography  Save this article

Relativistic chaos in the anisotropic harmonic oscillator

Author

Listed:
  • Vieira, Ronaldo S.S.
  • Michtchenko, Tatiana A.

Abstract

The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in Newtonian mechanics, whether forced, damped or multidimensional. On the other hand, it is known that relativistic, one-dimensional driven oscillators present chaotic behavior. However, there is no analogous result in the literature concerning relativistic conservative, two-dimensional oscillators. We consider in this paper different separable potentials for two-dimensional oscillators in the context of special relativistic dynamics. We show, by means of different chaos indicators, that all these systems present chaotic behavior under specific initial conditions. In particular, the relativistic anisotropic, two-dimensional harmonic oscillator is chaotic. The non-integrability of the system is shown to come from the momentum coupling in the kinetic part of the Hamiltonian, even if there are no coupling terms in the potential. It follows that chaos must appear in most integrable classical systems once we introduce relativistic corrections to the dynamics. The chaotic nature of the relativistic, anisotropic harmonic oscillator may be detected in the laboratory using Bose condensates in a two-dimensional optical lattice, extending the recent experiments on the one-dimensional case.

Suggested Citation

  • Vieira, Ronaldo S.S. & Michtchenko, Tatiana A., 2018. "Relativistic chaos in the anisotropic harmonic oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 276-282.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:276-282
    DOI: 10.1016/j.chaos.2018.10.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791830612X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.10.027?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.

    References listed on IDEAS

    as
    1. I. Chiorescu & P. Bertet & K. Semba & Y. Nakamura & C. J. P. M. Harmans & J. E. Mooij, 2004. "Coherent dynamics of a flux qubit coupled to a harmonic oscillator," Nature, Nature, vol. 431(7005), pages 159-162, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Skagerstam, Bo-Sture K., 2006. "On collective effects in cavity quantum electrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 314-326.

    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:117:y:2018:i:c:p:276-282. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.