IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v127y1984i1p173-193.html
   My bibliography  Save this article

Diffusion in a potential field: Path-integral approach

Author

Listed:
  • Baibuz, V.F.
  • Zitserman, V.Yu.
  • Drozdov, A.N.

Abstract

Within the framework of the path-integral formalism we develop a simple method to solve the Fokker-Planck diffusion problems in a potential field, including the decay of an unstable state. Unlike previous approaches, it yields a unified treatment of all time regimes, and is legitimate for any value of the diffusion coefficient. An attractive feature of our method is that it provides numerical results in regions where there are no analytical solutions. In particular, being valid for an arbitrary shape of the potential, it is very useful for studying a diffusion problem near and in the critical point where the standard treatments break down. Moreover, our method, after a simple transformation, permits to obtain also the first passage times of the process.

Suggested Citation

  • Baibuz, V.F. & Zitserman, V.Yu. & Drozdov, A.N., 1984. "Diffusion in a potential field: Path-integral approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(1), pages 173-193.
    • Handle: RePEc:eee:phsmap:v:127:y:1984:i:1:p:173-193
    DOI: 10.1016/0378-4371(84)90126-2
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437184901262
    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(84)90126-2?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. Tomita, Kazuhisa & Todani, Takao & Kidachi, Hideyuki, 1976. "Irreversible circulation and the undamped spiking in lasers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(2), pages 350-370.
    2. Caroli, B. & Caroli, C. & Roulet, B. & Saint-James, D., 1981. "On fluctuations and relaxation in systems described by a one-dimensional Fokker-Planck equation with a time-dependent potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(1), pages 233-256.
    3. Edholm, O. & Leimar, O., 1979. "The accuracy of Kramers' theory of chemical kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 313-324.
    4. 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.
    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. Schraiber, Joshua G., 2014. "A path integral formulation of the Wright–Fisher process with genic selection," Theoretical Population Biology, Elsevier, vol. 92(C), pages 30-35.
    2. 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.
    3. Kumar, Vinod & Menon, S.V.G., 1987. "Branch selectivity in a system crossing a bifurcation point: Fokker-Planck equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(2), pages 574-584.

    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. 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.
    2. 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 80-98.
    3. 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.
    4. Pavlova, E.G. & Aktaev, N.E. & Gontchar, I.I., 2012. "Modified Kramers formulas for the decay rate in agreement with dynamical modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6084-6100.
    5. Coffey, W.T. & Crothers, D.S.F. & Kalmykov, Yu.P. & Waldron, J.T., 1995. "Exact solution for the extended Debye theory of dielectric relaxation of nematic liquid crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(4), pages 551-575.
    6. Shimizu, T., 1978. "Theory of the relaxation and fluctuation from unstable and metastable states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 534-548.
    7. 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.
    8. Khait, Y.L., 1980. "Further development of the kinetic many-body concept of large energy fluctuations and rate processes in solids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 1-34.
    9. Malakhov, A.N. & Pankratov, A.L., 1996. "Exact solution of Kramers' problem for piecewise parabolic potential profiles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(1), pages 109-126.
    10. Dykman, M.I. & Krivoglaz, M.A., 1980. "Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 480-494.

    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:127:y:1984:i:1:p:173-193. 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.