IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v132y1985i2p357-374.html
   My bibliography  Save this article

Brownian motion in the bistable potential at intermediate and high friction: Relaxation from the instability point

Author

Listed:
  • Bunde, Armin
  • Gouyet, Jean-François

Abstract

We consider a Brownian particle in a double-well potential at intermediate and high friction and study the evolution of an initial distribution which is located at the top of the barrier. The evolution equation is obtained from the Fokker-Planck-Klein-Kramers equation by an inverse friction expansion and is transformed to a time-dependent Schrödinger equation which we solve approximately using the WKB method. The result becomes exact for temperatures low compared with the barrier height. We calculate explicitly the characteristic time in which the distribution changes from a single peak to a double peak structure and show that the decay process is mainly described by a scaling-function which reduces to Suzuki's scaling solution in the limit of high friction.

Suggested Citation

  • Bunde, Armin & Gouyet, Jean-François, 1985. "Brownian motion in the bistable potential at intermediate and high friction: Relaxation from the instability point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 357-374.
    • Handle: RePEc:eee:phsmap:v:132:y:1985:i:2:p:357-374
    DOI: 10.1016/0378-4371(85)90016-0
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437185900160
    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(85)90016-0?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. de Vries, S. & de Bundel, E. R. J. F., 1984. "The new, fourth edition of the IPC," World Patent Information, Elsevier, vol. 6(2), pages 58-62.
    2. Skinner, James L. & Wolynes, Peter G., 1979. "Derivation of Smoluchowski equations with corrections for Fokker-Planck and BGK collision models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 96(3), pages 561-572.
    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. Benoit, Magali & Jullien, Rémi, 1994. "Phase transition in the 2D ballistic growth model with quenched disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(4), pages 500-516.
    2. Gouyet, J.-F., 1992. "Anti-red bonds distribution law in 3D percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 301-308.
    3. Gouyet, J.F. & Rosso, M. & Clément, E. & Baudet, C. & Hulin, J.P., 1989. "Invasion of a porous medium under gravity: A quantitative analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 497-498.
    4. Hansen, Alex & Roux, Stéphane, 1989. "A geometrical interpretation of the chaotic state of inhomogeneous deterministic cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 275-297.
    5. 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.
    6. Gouyet, J.F. & Sapoval, B. & Boughaleb, Y. & Rosso, M., 1989. "Structure of noise generated on diffusion fronts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 620-624.

    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. Titulaer, U.M., 1980. "Corrections to the Smoluchowski equation in the presence of hydrodynamic interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(2), pages 251-265.
    2. 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.
    3. Janssen, J.A.M., 1988. "Solution of Kramers' problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(1), pages 145-176.
    4. Marchesoni, Fabio & Grigolini, Paolo, 1983. "The Kramers model of chemical relaxation in the presence of a radiation field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 269-285.
    5. Felderhof, B.U., 1983. "Reciprocity in electrohydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 383-396.
    6. Vollmer, H.D. & Risken, H., 1982. "Eigenvalues and eigenfunctions of the Kramers equation. Application to the Brownian motion of a pendulum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(1), pages 106-127.
    7. Widder, M.E. & Titulaer, U.M., 1989. "Brownian motion in a medium with inhomogeneous temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 154(3), pages 452-466.

    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:132:y:1985:i:2:p:357-374. 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.