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Condensed Matter > Statistical Mechanics
Title: First-Passage Duality
(Submitted on 19 Jul 2018 (v1), revised 27 Aug 2018 (this version, v2), latest version 22 Mar 2024 (v4))
Abstract: We show that the distribution of times for a diffusing particle to first hit an absorber is \emph{independent} of the direction of an external flow field (with the caveat that for flow away from the absorber, the hitting time is conditioned on the particle actually reaching the absorber). Thus in one dimension, the average time for a particle to travel to an absorber a distance $\ell$ away is $\ell/|v|$, \emph{independent} of the sign of $v$. This duality extends to all moments of the hitting time. In two dimensions, the distribution of first-passage times to an absorbing circle in the radial velocity field $v(r)=Q/(2\pi r)$ again exhibits duality. Our approach also gives a new perspective on how varying the radial velocity is equivalent to changing the spatial dimension, as well as the transition between transience and strong transience in diffusion.
Submission history
From: Sidney Redner [view email][v1] Thu, 19 Jul 2018 21:58:10 GMT (19kb,D)
[v2] Mon, 27 Aug 2018 00:44:03 GMT (30kb,D)
[v3] Fri, 14 Sep 2018 15:22:54 GMT (30kb,D)
[v4] Fri, 22 Mar 2024 18:26:57 GMT (30kb,D)
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