Stretched-exponential behavior and random walks on diluted hypercubic lattices
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Amer Physical Soc
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American Physical Society (APS)
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Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large-scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions N up to N = 28. We show that at long times both relaxation functions can be described by stretched exponentials with exponent 1/3 and a characteristic relaxation time which grows exponentially with dimension N. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model.
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Physical Review E. College Pk: Amer Physical Soc, v. 84, n. 4, p. 6, 2011.
