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Non-self-averaging behaviors and ergodicity in quenched trap models with finite system sizes
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Description
Tracking tracer particles in heterogeneous environments plays an important role in unraveling the material properties. These heterogeneous structures are often static and depend on the sample realizations. Sample-to-sample fluctuations of such disorder realizations sometimes become considerably large. When we investigate the sample-to-sample fluctuations, fundamental averaging procedures are a thermal average for a single disorder realization and the disorder average for different disorder realizations. Here, we report on non-self-averaging phenomena in quenched trap models with finite system sizes, where we consider the periodic and the reflecting boundary conditions. Sample-to-sample fluctuations of diffusivity greatly exceeds trajectory-to-trajectory fluctuations of diffusivity in the corresponding annealed model. For a single disorder realization, the time-averaged mean square displacement and position-dependent observables converge to constants with the aid of the existence of the equilibrium distribution. This is a manifestation of ergodicity. As a result, the time-averaged quantities do not depend on the initial condition nor on the thermal histories but depend crucially on the disorder realization.
12 pages, 7 figures
Journal
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- Physical Review E
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Physical Review E 97 (5), 052143-, 2018-05-30
American Physical Society (APS)