Asymptotics for the survival probability of a Rouse chain monomer

TL;DR

This paper analyzes the long-time behavior of the survival probability of a monomer in a Rouse chain with absorbing boundaries, revealing it follows a stretched-exponential decay due to anomalous diffusion.

Contribution

It provides the first detailed asymptotic analysis of the survival probability for a monomer in a Rouse chain with fixed boundaries, highlighting the stretched-exponential decay behavior.

Findings

Survival probability decays as a stretched exponential in time.

The mean-square displacement scales as t^{1/2}, indicating anomalous diffusion.

All moments of the first exit time distribution are finite.

Abstract

We study the long-time asymptotical behavior of the survival probability P_t of a tagged monomer of an infinitely long Rouse chain in presence of two fixed absorbing boundaries, placed at x = \pm L. Mean-square displacement of a tagged monomer obeys \bar{X^2(t)} \sim t^{1/2} at all times, which signifies that its dynamics is an anomalous diffusion process. Constructing lower and upper bounds on P_t, which have the same time-dependence but slightly differ by numerical factors in the definition of the characteristic relaxation time, we show that P_t is a stretched-exponential function of time, \ln(P_t) \sim - t^{1/2}/L^2. This implies that the distribution function of the first exit time from a fixed interval [-L,L] for such an anomalous diffusion has all moments.