IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v179y1991i1p103-130.html
   My bibliography  Save this article

Phase variable and phase relaxation processes in the Liouville space

Author

Listed:
  • Ban, Masashi

Abstract

The quantum dissipative dynamics of a phase variable is studied. A phase variable is treated as a quantum mechanical operator in Liouville space. The time translation properties of a phase operator and its eigenstate are investigated in terms of a time-evolution generator describing the phase relaxation process. The model corresponds to a quantum mechanical generalization of the random frequency modulation. An arbitrary state of a system can be expressed in terms of superpositions of the eigenstates of a phase operator. It is found that the width of a wave packet expressed by the phase eigenstates spreads monotonously with time, and that any stationary state is a completely random phase state. Such a phase randomizing process makes the entropy of a system increase. This process is also discussed with regard to stochastic processes. The Langevin equation for the phase variable and the Fokker-Planck equation for the probability distribution function in the phase eigenspace are obtained.

Suggested Citation

  • Ban, Masashi, 1991. "Phase variable and phase relaxation processes in the Liouville space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(1), pages 103-130.
  • Handle: RePEc:eee:phsmap:v:179:y:1991:i:1:p:103-130
    DOI: 10.1016/0378-4371(91)90217-Z
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719190217Z
    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(91)90217-Z?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. Arimitsu, T. & Pradko, J. & Umezawa, H., 1986. "Generating functional methods in non-equilibrium thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 487-504.
    2. Ban, Masashi & Arimitsu, Toshihico, 1985. "A solvable model of microscopic frequency modulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(3), pages 455-468.
    3. Arimitsu, T. & Sudo, Y. & Umezawa, H., 1987. "Dynamical rearrangement of the thermal vacuum in thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 433-451.
    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. Arimitsu, T. & Willeboordse, H.F. & Iwasaki, T., 1992. "An analytical treatment of a localized electronphonon system in terms of non-equilibrium thermo field dynamics: Intensity distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 214-227.
    2. Arimitsu, T. & Ban, M. & Saito, T., 1991. "Stochastic Liouville equation approach within non-equilibrium thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 177(1), pages 329-338.
    3. Tominaga, T. & Arimitsu, T. & Pradko, J. & Umezawa, H., 1988. "A derivation of the laser master equation in terms of thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(1), pages 97-117.
    4. Arimitsu, Toshihico, 1988. "Kinetic equations within the formalism of non-equilibrium thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(3), pages 427-455.
    5. Tominaga, T. & Ban, M. & Arimitsu, T. & Pradko, J. & Umezawa, H., 1988. "Spin relaxation in terms of thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(1), pages 26-48.
    6. Laciana, Carlos E., 1995. "Can gravity be a thermal reservoir?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 511-517.
    7. Arimitsu, Toshihico, 1989. "Non-equilibrium open systems and non-equilibrium thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 158(1), pages 317-325.
    8. Arimitsu, T. & Guida, M. & Umezawa, H., 1988. "Dissipative quantum field theory -thermo field dynamics-," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(1), pages 1-26.
    9. Ban, Masashi, 1994. "Phase operator formalism in thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(3), pages 327-356.
    10. Arimitsu, T. & Sudo, Y. & Umezawa, H., 1987. "Dynamical rearrangement of the thermal vacuum in thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 433-451.

    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:179:y:1991:i:1:p:103-130. 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.