Non-self-averaging behaviors and ergodicity in quenched trap models with finite system sizes

Takuma Akimoto, Eli Barkai, Keiji Saito

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Tracking tracer particles in heterogeneous environments plays an important role in unraveling 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 exceed 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 because of the existence of the equilibrium distribution. This is a manifestation of ergodicity. As a result, the time-averaged quantities depend neither on the initial condition nor on the thermal histories but depend crucially on the disorder realization.

Original languageEnglish
Article number052143
JournalPhysical Review E
Issue number5
Publication statusPublished - 2018 May 30

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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