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Diffusion in a potential field: Path-integral approach

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
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    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.

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