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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    4. 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.
    5. 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.
    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.

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