Non-self-averaging behaviors and ergodicity in quenched trap model with finite system size

Abstract

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

References in corpus (9)

• Anomalous transport in the crowded world of biological cells
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Occupation Time Statistics in the Quenched Trap Model
• Weakly non-ergodic Statistical Physics
• Anomalous diffusion in a quenched-trap model on fractal lattices
• Non-Gaussian diffusion in static disordered media
• Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

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