IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v412y2014icp92-100.html
   My bibliography  Save this article

The Fokker–Planck equation for a bistable potential

Author

Listed:
  • Caldas, Denise
  • Chahine, Jorge
  • Filho, Elso Drigo

Abstract

The Fokker–Planck equation is studied through its relation to a Schrödinger-type equation. The advantage of this combination is that we can construct the probability distribution of the Fokker–Planck equation by using well-known solutions of the Schrödinger equation. By making use of such a combination, we present the solution of the Fokker–Planck equation for a bistable potential related to a double oscillator. Thus, we can observe the temporal evolution of the system describing its dynamic properties such as the time τ to overcome the barrier. By calculating the rates k=1/τ as a function of the inverse scaled temperature 1/D, where D is the diffusion coefficient, we compare the aspect of the curve k×1/D, with the ones obtained from other studies related to four different kinds of activated process. We notice that there are similarities in some ranges of the scaled temperatures, where the different processes follow the Arrhenius behavior. We propose that the type of bistable potential used in this study may be used, qualitatively, as a simple model, whose rates share common features with the rates of some single rate-limited thermally activated processes.

Suggested Citation

  • Caldas, Denise & Chahine, Jorge & Filho, Elso Drigo, 2014. "The Fokker–Planck equation for a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 92-100.
    • Handle: RePEc:eee:phsmap:v:412:y:2014:i:c:p:92-100
    DOI: 10.1016/j.physa.2014.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114004749
    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/j.physa.2014.06.009?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. Lee, Kwonmoo & Sung, Wokyung, 2002. "Ion transport and channel transition in biomembranes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 79-97.
    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. Philipp, Lucas & Shizgal, Bernie D., 2019. "A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 158-166.
    2. Polotto, Franciele & Drigo Filho, Elso & Chahine, Jorge & Oliveira, Ronaldo Junio de, 2018. "Supersymmetric quantum mechanics method for the Fokker–Planck equation with applications to protein folding dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 286-300.
    3. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    4. Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    5. Rui, Weiguo & Yang, Xinsong & Chen, Fen, 2022. "Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    6. Drigo Filho, Elso & Chahine, Jorge & Araujo, Marcelo Tozo & Ricotta, Regina Maria, 2022. "Probability distribution to obtain the characteristic passage time for different tri-stable potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).

    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. Ramírez-Piscina, L. & Sancho, J.M., 2018. "Periodic spiking by a pair of ionic channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 345-354.
    2. Polotto, Franciele & Drigo Filho, Elso & Chahine, Jorge & Oliveira, Ronaldo Junio de, 2018. "Supersymmetric quantum mechanics method for the Fokker–Planck equation with applications to protein folding dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 286-300.
    3. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).

    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:412:y:2014:i:c:p:92-100. 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.