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On fluctuations and relaxation in systems described by a one-dimensional Fokker-Planck equation with a time-dependent potential

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  • Caroli, B.
  • Caroli, C.
  • Roulet, B.
  • Saint-James, D.

Abstract

We study the effect of a time variation of a bistable potential on Kramers relaxation and on Suzuki's fluctuation enhancement, for a system described by a one-variable Fokker-Planck equation, in the limit of a small constant diffusion coefficient. We show that the two processes must be described with two different approximations: 1.(i) Kramers relaxation can be treated in a quasi-adiabatic scheme. We then show that, for a large range of potential modulation rates, the local populations in each well obey adiabatic balance equations, the solution of which we discuss in various limits.2.(ii) Suzuki's description of the fluctuation enhancement can be extended to the dynamical case. We reformulate the technique set up by Ahlers et al. to describe the crossing of the bifurcation from a mono- to a bistable potential. We show that the extended Suzuki approximation is valid provided that the crossing velocity is larger than a limit which we estimate.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:108:y:1981:i:1:p:233-256
    DOI: 10.1016/0378-4371(81)90177-1
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    Cited by:

    1. 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.
    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.

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