IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v214y1995i4p619-628.html
   My bibliography  Save this article

Generalized nonlinear Doebner-Goldin Schrödinger equation and the relaxation of quantum systems

Author

Listed:
  • Dodonov, V.V.
  • Mizrahi, S.S.

Abstract

We propose a new class of nonlinear homogeneous extension of the Doebner-Goldin Schrödinger equation, valid for arbitrary representations and operators, chosen in accordance with the investigated physical problem. We verify that the nonlinearity simulates an environment, thence, the new model leads to simple exact solutions as, for instance, the time-dependent squeezed coherent states and a special class of stationary states that we call pseudothermal, reached after relaxation. We illustrate the use of the new equation with applications to problems such as, the relaxation of a two-level or spin-1/2 system, and of the harmonic oscillator (HO) or equivalently, the emission-absorption process of photons in an electromagnetic cavity. Furthermore, in order to compare solutions for the HO example we introduce two different representations in the new equation, one continuous (positional representation) and the other discrete (Fock states).

Suggested Citation

  • Dodonov, V.V. & Mizrahi, S.S., 1995. "Generalized nonlinear Doebner-Goldin Schrödinger equation and the relaxation of quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(4), pages 619-628.
    • Handle: RePEc:eee:phsmap:v:214:y:1995:i:4:p:619-628
    DOI: 10.1016/0378-4371(94)00239-P
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719400239P
    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)00239-P?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. Mizrahi, Salomon S. & Marchiolli, Marcelo A., 1993. "Pseudo-diffusion equation and information entropy of squeezed-coherent states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(1), pages 96-115.
    2. Hayes, Kathy & Slottje, D. J. & Porter-Hudak, Susan & Scully, Gerald, 1990. "Is the size distribution of income a random walk?," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 213-226.
    3. Syed Barakat Ahmad, 1973. "India and Palestine 1896–1947: The Genesis of a Foreign Policy," India Quarterly: A Journal of International Affairs, , vol. 29(4), pages 300-307, October.
    4. Popov, V.M. & Tataru, N.N. & Bajenesco, T.I., 1968. "Quelques solutions originales utilisees dans la construction d'une grande calculatrice analogique," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 10(4), pages 211-213.
    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. Portesi, M & Plastino, A, 1996. "Generalized entropy as a measure of quantum uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 412-430.
    2. Sophia Dimelis & Alexandra Livada, 1999. "Inequality and business cycles in the U.S. and European Union countries," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 5(3), pages 321-338, August.
    3. Laurence J. Kotlikoff, 2007. "Staticide - America's Suicidal Healthcare Status Quo," Boston University - Department of Economics - Working Papers Series WP2007-014, Boston University - Department of Economics.
    4. repec:ebl:ecbull:v:3:y:2004:i:29:p:1-9 is not listed on IDEAS
    5. Marchiolli, Marcelo A., 2003. "Nonclassical statistical properties of finite-coherent states in the framework of the Jaynes–Cummings model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 331-354.
    6. Simon Parker, 1998. "Is the inequality of lifetime wealth a random walk?," Applied Economics Letters, Taylor & Francis Journals, vol. 5(8), pages 523-525.
    7. Lawrence E. Raffalovich, 1994. "Detrending Time Series," Sociological Methods & Research, , vol. 22(4), pages 492-519, May.
    8. Baotai Wang & Tomson Ogwang, 2004. "Is the Size Distribution of Income in Canada a Random Walk?," Economics Bulletin, AccessEcon, vol. 3(29), pages 1-9.
    9. Chun‐Yu Ho & Dan Li, 2008. "Rising regional inequality in China: Policy regimes and structural changes," Papers in Regional Science, Wiley Blackwell, vol. 87(2), pages 245-259, June.
    10. John A. Bishop & Haiyong Liu & Lester A. Zeager & Yizhen Zhao, 2020. "Revisiting macroeconomic activity and income distribution in the USA," Empirical Economics, Springer, vol. 59(3), pages 1107-1125, September.

    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:4:p:619-628. 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.