Abstract
The diffusion over a simple parabolic barrier is exactly solved with a non-Markovian Generalized Langevin Equation. For a short relaxation time, the problem is shown to be similar to a Markovian one, with a smaller effective friction. But for longer relaxation time, the average trajectory starts to oscillate and the system can have a very fast first passage over the barrier. For very long relaxation times, the solution tends to a zero-friction limit.
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PACS: 02.50.EY, 05.40.−a, 25.70.Jj
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Boilley, D., Lallouet, Y. Non-Markovian Diffusion Over a Saddle with a Generalized Langevin Equation. J Stat Phys 125, 473–489 (2006). https://doi.org/10.1007/s10955-006-9197-5
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DOI: https://doi.org/10.1007/s10955-006-9197-5