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Yilmaz B, Ayik S, Abe Y, et al. Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function. Phys Rev E Stat Nonlin Soft Matter Phys. 2008;77(1):011121doi: 10.1103/PhysRevE.77.011121.
Yilmaz, B., Ayik, S., Abe, Y., & Boilley, D. (2008). Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function. Physical review. E, Statistical, nonlinear, and soft matter physics, 77(1), 011121. https://doi.org/10.1103/PhysRevE.77.011121
Yilmaz, B, et al. "Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 77,1 (2008): 011121. doi: https://doi.org/10.1103/PhysRevE.77.011121
Yilmaz B, Ayik S, Abe Y, Boilley D. Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function. Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1):011121. doi: 10.1103/PhysRevE.77.011121. Epub 2008 Jan 22. PMID: 18351832.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1):011121. doi: 10.1103/PhysRevE.77.011121. Epub 2008 Jan 22.

Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function.

Physical review. E, Statistical, nonlinear, and soft matter physics

B Yilmaz, S Ayik, Y Abe, D Boilley

Affiliations

  1. Physics Department, Ankara University, 06100 Ankara, Turkey.

PMID: 18351832 DOI: 10.1103/PhysRevE.77.011121

Abstract

The over-passing probability across an inverted parabolic potential barrier is investigated according to the classical and quantal generalized Langevin equations. It is shown that, in the classical case, the asymptotic value of the over-passing probability is determined by a single dominant root of the "characteristic function," and it is given by a simple expression. The expression for the over-passing probability is quite general, and details of dissipation mechanism and memory effects enter into the expression only through the dominant root of the characteristic equation.

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