TY - JOUR
T1 - Non-self-averaging behaviors and ergodicity in quenched trap models with finite system sizes
AU - Akimoto, Takuma
AU - Barkai, Eli
AU - Saito, Keiji
N1 - Funding Information:
T.A. was partially supported by the Grant-in-Aid for Scientific Research (B) of the JSPS, Grant No. 16KT0021. This research was supported by the Israel Science Foundation (E.B.) grant 1898/17. K.S. was supported by JSPS Grants-in-Aid for Scientific Research (No. JP25103003, JP16H02211, and JP17K05587).
Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/5/30
Y1 - 2018/5/30
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85048153316&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85048153316&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.97.052143
DO - 10.1103/PhysRevE.97.052143
M3 - Article
C2 - 29906876
AN - SCOPUS:85048153316
VL - 97
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
SN - 1063-651X
IS - 5
M1 - 052143
ER -