2018/02/28 by Takuma Akimoto, Eli Barkai, Keiji Saito
Materials Science · Mathematics · Physics and Astronomy · #Boundary value problem #Ergodicity #Fractional Differential Equations Solutions #Material Dynamics and Properties #Mathematics #Mean squared displacement #Molecular dynamics #Observable #Periodic boundary conditions #Physics #Position (finance) #Quantum mechanics #Realization (probability) #Sample (material) #Statistical physics #Statistics #Theoretical and Computational Physics #Thermal diffusivity #Thermodynamics #Trajectory #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.97.052143
published as Phys. Rev. E 97, 052143 (2018) · 12 pages, 7 figures
openalex publication_date 2018/05/30 · arxiv created 2019/01/03 · arxiv updated 2019/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.