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Cyclization of a Polymer: A First Passage Problem for a Non-Markovian Process

I. M. Sokolov
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Abstract

We discuss a problem of cyclization of a polymer molecule, which is an important example of reaction in a system showing strongly non-Markovian behavior on the timescales of interest. We show that the knowledge of the joint three-time probability distribution of the end-to-end distance is sufficient for the full description of the cyclization kinetics, so that the survival probability follows rigorously as a solution of the Volterra integral equation. The corresponding kinetics can easily be evaluated numerically. We moreover discuss how do some well-known approximations appear from this exact scheme due to decoupling.

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I. M. Sokolov. 2002-07-08. Cyclization of a Polymer: A First Passage Problem for a Non-Markovian Process. https://doi.org/10.1103/physrevlett.90.080601

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