IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-31338-2_2.html
   My bibliography  Save this book chapter

Quasimodes in Integrable Systems and Semi-Classical Limit

In: Essays in Mathematics and its Applications

Author

Listed:
  • M. Baldo

    (INFN, Sezione di Catania)

  • F. Raciti

    (University of Catania, Department of Mathematics and Computer Science)

Abstract

Quasimodes are long-living quantum states that are localized along classical orbits. They can be considered as resonances, whose wave functions display semi-classical features. In some integrable systems, they have been constructed mainly by the coherent state method, and their connection with the classical motion has been extensively studied, in particular as a tool to perform the semi-classical limit of a quantum system. In this work, we present a method to construct quasimodes in integrable systems. Although the method is based on elementary procedures, it is quite general. It is shown that the requirement of a long lifetime and strong localization implies that the quasimode must be localized around a closed classical orbit. At a fixed degree of localization, the lifetime of the quasimode can be made arbitrarily longer with respect to the classical period in the asymptotic limit of large quantum numbers. It turns out that the coherent state method is a particular case of this general scheme.

Suggested Citation

  • M. Baldo & F. Raciti, 2016. "Quasimodes in Integrable Systems and Semi-Classical Limit," Springer Books, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Essays in Mathematics and its Applications, pages 25-47, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31338-2_2
    DOI: 10.1007/978-3-319-31338-2_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-319-31338-2_2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.