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

Takuma Akimoto, Eli Barkai, Keiji Saitou

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume97
Issue number5
DOIs
Publication statusPublished - 2018 May 30

Fingerprint

Ergodicity
Trap
Averaging
Disorder
traps
disorders
Fluctuations
Diffusivity
diffusivity
Model
trajectories
Trajectory
Particle Tracking
Heterogeneous Environment
Equilibrium Distribution
Material Properties
Mean Square
tracers
Exceed
Initial conditions

ASJC Scopus subject areas

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

Cite this

Non-self-averaging behaviors and ergodicity in quenched trap models with finite system sizes. / Akimoto, Takuma; Barkai, Eli; Saitou, Keiji.

In: Physical Review E, Vol. 97, No. 5, 052143, 30.05.2018.

Research output: Contribution to journalArticle

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