**Continuous-time random-walk approach to supercooled liquids. II. Mean-
square displacements in polymer melts**

J Helfferich and F Ziebert and S Frey and H Meyer and J Farago and A Blumen and J Baschnagel, PHYSICAL REVIEW E, 89, 042604 (2014).

DOI: 10.1103/PhysRevE.89.042604

The continuous-time random walk (CTRW) describes the single-particle
dynamics as a series of jumps separated by random waiting times. This
description is applied to analyze trajectories from molecular dynamics
(MD) simulations of a supercooled polymer melt. Based on the algorithm
presented by Helfferich et al. **Phys. Rev. E 89, 042603 (2014)**, we
detect jump events of the monomers. As a function of temperature and
chain length, we examine key distributions of the CTRW: the jump-length
distribution (JLD), the waiting-time distribution (WTD), and the
persistence-time distribution (PTD), i.e., the distribution of waiting
times for the first jump. For the equilibrium (polymer) liquid under
consideration, we verify that the PTD is determined by the WTD. For the
mean-square displacement (MSD) of a monomer, the results for the CTRW
model are compared with the underlying MD data. The MD data exhibit two
regimes of subdiffusive behavior, one for the early a process and
another at later times due to chain connectivity. By contrast, the
analytical solution of the CTRW yields diffusive behavior for the MSD at
all times. Empirically, we can account for the effect of chain
connectivity in Monte Carlo simulations of the CTRW. The results of
these simulations are then in good agreement with the MD data in the
connectivity-dominated regime, but not in the early a regime where they
systematically underestimate the MSD from the MD.

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