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Decoupling of exchange and persistence times in atomistic models of glass formers
14.The decoupling of the different relevant relaxation rates is also evident from the behavior of four-point dynamic susceptibilities at different length scales, see, for example Refs. 10, 15, and 16.
17.L. Maibaum, Ph.D. thesis, University of California Berkeley, 2005.
21.Molecular dynamics simulations were performed using a microcanonical Verlet algorithm for Fig. 1 and LAMMPS (Ref. 22) for Fig. 2, at temperatures along a constant density path. The particle numbers and box length, and for Fig. 1, and and for Fig. 2, were fixed in each run. The system was prepared at each thermodynamic state point by coupling to a heat bath for time using velocity rescaling or velocity reassigning every 50 time steps. No drift or aging was observed over the equilibration time in thermodynamic or dynamic observables before performing production runs. Both and were significantly longer than the structural relaxation time.
24.In the context of renewal processes (Ref. 25), exchange and persistence times are called total and excess lifetimes, respectively. If events occur over a very short time scale as compared to waiting times the distributions of persistence and exchange times are related by (Refs. 6 and 25). In our case, where an event may be built up over time (a displacement of distance does not occur instantaneously), this relation works only as an approximation. Nevertheless, application of this formula gives reasonable estimates of the behavior.
25.G. Grimmett and D. Stirzaker, Probability and Random Processes (Oxford University Press, Oxford, 2001).
26.The distributions of persistence (or first-passage) times for smaller cutoff distances behave differently, see P. Allegrini, J. F. Douglas, and S. C. Glotzer, Phys. Rev. E 60, 5714 (1999). These authors also find that the typical first-passage time for distances comparable to a particle diameter scales with temperature roughly as , which is consistent with what is expected from dynamic facilitation (Refs. 5 and 6).
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