IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v221y1995i4p539-553.html
   My bibliography  Save this article

The full solution of the independent oscillator model and the properties of the environment

Author

Listed:
  • Gu, Jian-zhong
  • Wu, Xi-zhen
  • Zhuo, Yi-zhong

Abstract

By using Laplace transformation, a set of analytic solutions of the coordinates and velocities for a system plus an environment are given. In the absence of system potential, based on the solutions, we rigorously prove that if the initial state of the composite system lies in its thermal equilibrium, then the environment is equipartition of energy, which, however, is moving with the system. At the same time, we discuss the time development of the mean square displacements, square velocities and the mean energies of both the system and the environment when the initial state is in partial thermal equilibrium or far away from thermal equilibrium. In addition, we also pay attention to the environmental behaviour when the initial state is deterministic. It is shown that the properties of the environment are quite different from those of the collection of oscillators discussed by Ford et al. (G.W. Ford, M. Kac and P Mazur, J. Math. Phys. 6 (1965) 504).

Suggested Citation

  • Gu, Jian-zhong & Wu, Xi-zhen & Zhuo, Yi-zhong, 1995. "The full solution of the independent oscillator model and the properties of the environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(4), pages 539-553.
    • Handle: RePEc:eee:phsmap:v:221:y:1995:i:4:p:539-553
    DOI: 10.1016/0378-4371(95)00196-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437195001968
    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(95)00196-8?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. Micheline Thomine-Desmazures, 1965. "L'investigation psychosociologique en milieu rural," Économie rurale, Programme National Persée, vol. 64(1), pages 19-24.
    2. Caldeira, Gregory A., 1990. "Public Opinion and the Supreme Court. By Thomas R. Marshall. Boston: Unwin Hyman, 1989. 214p. $39.95 cloth, $14.95 paper," American Political Science Review, Cambridge University Press, vol. 84(2), pages 663-664, June.
    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. Remaud, B. & Hernández, E.S., 1981. "On the phase-space dynamics of a time-dependent harmonic oscillator at finite temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(3), pages 553-566.
    2. Braun, E., 1980. "A model of Brownian dynamics for colloidal suspensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 325-342.
    3. Dekker, H., 1987. "Quantum mechanical barrier problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 387-395.
    4. Dekker, H., 1988. "Incoherent tunneling at weak bias: Strong quantum damping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 154(1), pages 61-88.
    5. Gorini, Vittorio & Verri, Maurizio & Frigerio, Alberto, 1989. "Non-markovian behavior in low-temperature damping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 161(2), pages 357-384.
    6. Dekker, H., 1991. "Multisite spin hopping analysis of multilevel dissipative quantum tunneling and coherence at finite temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(1), pages 81-102.
    7. Lindenberg, Katja & Mohanty, Udayan & Seshadri, V., 1983. "Hamiltonian model for the Brownian motion of a rigid rotor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 1-16.
    8. Kagermann, H., 1982. "Stochastic equations arising from test particle problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 199-206.
    9. Yannouleas, C., 1985. "Quantal Brownian motion from RPA dynamics: The master and Fokker-Planck equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(1), pages 1-27.
    10. Yannouleas, C., 1984. "The RPA description of the quantum damped harmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 549-576.
    11. Dekker, H., 1987. "Dissipative quantum mechanics: A proof of dynamical consistency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(2), pages 445-452.
    12. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
    13. Sánchez Cañizares, J. & Sols, F., 1994. "Translational symmetry and microscopic preparation in oscillator models of quantum dissipation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(1), pages 181-193.
    14. Cáceres, Manuel O. & Chattah, Ana K., 1996. "On the Schrödinger-Langevin picture and the master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 234(1), pages 322-340.
    15. Tegmark, Max & Yeh, Leehwa, 1994. "Steady states of harmonic oscillator chains and shortcomings of harmonic heat baths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 342-362.
    16. Bafaluy, J. & Rubí, J.M., 1988. "The “harmonic liquid” away from equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 153(1), pages 129-146.
    17. Eckhardt, W., 1987. "On the consistent description of quantum relaxation processes: The harmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(1), pages 81-110.
    18. Kagermann, H., 1981. "Stochastic equations arising from test particle problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(3), pages 365-379.
    19. Dekker, H., 1985. "A contribution to the dynamical theory of radiating electrons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(1), pages 1-34.
    20. Hernández, E.S. & Mizrahi, S.S., 1983. "Parametrization of open systems with effective quadratic Hamiltonians plus stochastic force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 159-176.

    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:221:y:1995:i:4:p:539-553. 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.