IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v102y1980i3p470-488.html
   My bibliography  Save this article

Brownian motion of harmonic systems with fluctuating parameters

Author

Listed:
  • West, Bruce J.
  • Lindenberg, Katja
  • Seshadri, V.

Abstract

Exact first and second order statistics of a damped mechanical oscillator with a fluctuating frequency and driven by a fluctuating force are obtained. All the cumulants of the fluctuating frequency are assumed to be delta correlated, while those of the driving force are of arbitrary form. The oscillator results depend only on the first and second order statistics of the driving force and on the coefficients of the first and second cumulants of the frequency fluctuations. Thus neither the higher order statistics of the driving force nor the coefficients of the higher cumulants of the frequency fluctuations need to be specified. When the fluctuating quantities are both delta correlated, the dynamics of the correction functions are shown to be independent of the frequency fluctuations.

Suggested Citation

  • West, Bruce J. & Lindenberg, Katja & Seshadri, V., 1980. "Brownian motion of harmonic systems with fluctuating parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 470-488.
    • Handle: RePEc:eee:phsmap:v:102:y:1980:i:3:p:470-488
    DOI: 10.1016/0378-4371(90)90177-T
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719090177T
    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(90)90177-T?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. Rodríguez, R.F. & Van Kampen, N.G., 1976. "Systematic treatment of fluctuations in a nonlinear oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 347-362.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Schweitzer, Frank & Schimansky-Geier, Lutz & Ebeling, Werner & Ulbricht, Heinz, 1988. "A stochastic approach to nucleation in finite systems: Theory and computer simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(1), pages 261-279.
    2. Roerdink, J.B.T.M, 1982. "A cumulant expansion for the time correlation functions of solutions to linear stochastic differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 557-587.
    3. Roerdink, J.B.T.M., 1981. "Inhomogeneous linear random differential equations with mutual correlations between multiplicative, additive and initial-value terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 109(1), pages 23-57.
    4. van Kampen, N.G., 1980. "Process with delta-correlated cumulants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 489-495.
    5. Wissel, Christian, 1984. "Solution of the master equation of a bistable reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 150-163.
    6. Lindenberg, Katja & West, Bruce J., 1984. "Finite correlation time effects in nonequilibrium phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 25-47.
    7. Barcons, F.X. & Garrido, L., 1983. "Systems under the influence of white and colored poisson noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 212-226.

    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. Kondepudi, D.K. & Nelson, G.W., 1984. "Chiral-symmetry-breaking states and their sensitivity in nonequilibrium chemical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 465-496.
    2. Chechetkin, V.R. & Lutovinov, V.S. & Samokhin, A.A., 1991. "On the diffusion of passive impurities in random flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 87-113.
    3. Stewart, Glen R., 1982. "Long-time behavior of a non-Markovian Brownian oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 519-530.
    4. Gang, Hu, 1985. "Master equation without strict detailed balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 586-592.
    5. Henery, R.J., 1982. "The short-time evolution of a non-linear oscillator driven by white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 321-330.
    6. 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.
    7. Dekker, H., 1980. "On the path integral for diffusion in curved spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(3), pages 586-596.
    8. Shapiro, V.E. & Loginov, V.M., 1978. "“Formulae of differentiation” and their use for solving stochastic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 563-574.
    9. Kagermann, H., 1982. "Stochastic equations arising from test particle problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 199-206.
    10. Brey, J.J. & Casado, J.M. & Morillo, M., 1984. "Renormalized equations for a weakly nonlinear Duffing oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 481-496.
    11. Barcons, F.X. & Garrido, L., 1983. "Systems under the influence of white and colored poisson noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 212-226.
    12. 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. 178(2), pages 289-331.
    13. Dekker, H., 1980. "Critical dynamics the expansion of the master equation including a critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 55-79.
    14. Wulbrand, Wilhelm & Kagermann, Henning, 1985. "The influence of random temperature modulation on the convective instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 131(1), pages 182-196.
    15. Das, Amal K., 1979. "Stochastic diffusion in a periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(3), pages 528-544.
    16. Möbius, A. & Vojta, G., 1978. "Statistical theory of electron transport in open electron-phonon systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 94(2), pages 321-338.
    17. Marshall, T.W., 1980. "Brownian motion and quasi-Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 172-182.
    18. Gómez-Ordóñez, J. & Morillo, M., 1992. "Numerical analysis of the Smoluchowski equation using the split operator method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(4), pages 490-507.
    19. Roerdink, J.B.T.M, 1982. "A cumulant expansion for the time correlation functions of solutions to linear stochastic differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 557-587.
    20. Moreau, M. & Vicente, L., 1982. "Influence of an external field on the stochastic theory of polymerization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(3), pages 543-559.

    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:102:y:1980:i:3:p:470-488. 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.