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Abstract
How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the first-passage time statistics to a target zone in phase space with lower occupation probability. Here, we present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories. We apply our method to polymer systems, to determine (i) the first time for a flexible polymer to reach a large extension, and (ii) the first closure time of a stiff inextensible wormlike chain. Our results are in excellent agreement with numerical simulations and provide explicit asymptotic laws for the mean first-passage times to rarely visited configurations.
Highlights
Rapid CommunicationsWe present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories
How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited—typically because of a high energy cost? This question generally amounts to the determination of the first-passage time statistics to a target zone in phase space with lower occupation probability
We show that memory effects can be accounted for by characterizing the trajectory followed by r(t ) in the future of the first-passage time (FPT), which generalizes a recent theoretical approach restricted to unbiased Gaussian processes [15]
Summary
We present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories. In the context of large deviation kinetics of flexible polymers, it has recently [35] been noted that standard weak-noise theories (to be defined below) lead to erroneous scalings for the mean FPT. In this Rapid Communication, we investigate the impact of memory effects on the mean time a continuous nonMarkovian (possibly non-Gaussian) variable r(t ) takes to reach a given rarely visited threshold.
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