First passage time problems in time-dependent fields |
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Authors: | John E Fletcher Shlomo Havlin George H Weiss |
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Institution: | (1) Division of Computer Research and Technology, National Institutes of Health, 20892 Bethesda, Maryland;(2) Department of Physics, Bar-Ilan University, Ramat-Gan, Israel |
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Abstract: | This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency * for which the mean residence time on the line segment is a minimum. It is shown that for a random walk on a line segment of lengthL the mean residence time goes likeL
2 for largeL when ![piv](/content/v311536288l32525/xxlarge982.gif) ![ne](/content/v311536288l32525/xxlarge8800.gif) *, but when = * the dependence is proportional toL. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation. |
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Keywords: | Random walks diffusion processes first passage times residence times diffusive coherence |
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