IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v214y1995i2p295-308.html
   My bibliography  Save this article

The Heisenberg equation for phonon operators and soliton solutions in nonlinear lattices

Author

Listed:
  • Kitamura, Toyoyuki

Abstract

The Heisenberg equation for phonon operators in nonlinear lattices is derived establishing the interaction Hamiltonian included higher powers of particle-hole pairs in nonlinear lattices. A phonon operator consists of a particle-hole pair in the harmonic potential approximation in the two band model; it represents an up or down transition of atoms between two levels. Applying the boson transformation method to the Heisenberg equation for phonon operators, we obtain the classical dynamical equation and a linear equation with the self-consistent potential created by the extended objects in nonlinear lattices. The boson transformation leads to soliton solutions in the long wavelength limit. The linear equation can be used to obtain scattering states, bound states and translational modes for phonons.

Suggested Citation

  • Kitamura, Toyoyuki, 1995. "The Heisenberg equation for phonon operators and soliton solutions in nonlinear lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(2), pages 295-308.
    • Handle: RePEc:eee:phsmap:v:214:y:1995:i:2:p:295-308
    DOI: 10.1016/0378-4371(94)00229-M
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719400229M
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(94)00229-M?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. Kitamura, T. & Umezawa, H., 1983. "A quantum field theory of crystals near melting temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 38-58.
    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. Kitamura, Toyoyuki, 1988. "A quantum field theory of phonons and boiling in liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 303-317.
    2. Kitamura, Toyoyuki, 1992. "A quantum field theory of phonons in crystals extended to the multi-band model II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(1), pages 201-208.
    3. Lebedev, V.V. & Smilga, A.V., 1992. "Anomalous damping in plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 187-220.

    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:phsmap:v:214:y:1995:i:2:p:295-308. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.