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First-encounter time of two diffusing particles in confinement

Abstract : We investigate how confinement may drastically change both the probability density of the first-encounter time and the associated survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we focus on two one-dimensional settings: a half-line and an interval. We first consider the case with equal particle diffusivities, for which exact results can be obtained for the survival probability and the associated first-encounter time density valid over the full time domain. We also evaluate the moments of the first-encounter time when they exist. We then turn to the case with unequal diffusivities and focus on the long-time behavior of the survival probability. Our results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as the translational invariance of such systems is broken.
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Contributor : Denis Grebenkov Connect in order to contact the contributor
Submitted on : Tuesday, October 12, 2021 - 5:46:04 PM
Last modification on : Wednesday, November 3, 2021 - 6:37:53 AM


arXiv 2006.13563 (2020) Le Vot...
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F. Le Vot, S. B. Yuste, E. Abad, Denis Grebenkov. First-encounter time of two diffusing particles in confinement. Physical Review E , American Physical Society (APS), 2020, 102 (3), pp.032118. ⟨10.1103/PhysRevE.102.032118⟩. ⟨hal-03375459⟩



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