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Updated: Jun 2, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Intrinsic randomness of transport coefficient in subdiffusion with static disorder
Tomoshige Miyaguchi1, Takuma Akimoto
1Department of Applied Physics, Osaka City University, Osaka 558-8585, Japan. tomo@a-phys.eng.osaka-cu.ac.jp
Abstract:
Fluctuations in the time-averaged mean-square displacement for random walks on hypercubic lattices with static disorder are investigated. It is analytically shown that the diffusion coefficient becomes a random variable as a manifestation of weak ergodicity breaking. For two- and higher- dimensional systems, the distribution function of the diffusion coefficient is found to be the Mittag-Leffler distribution, which is the same as for the continuous-time random walk, whereas for one-dimensional systems a different distribution (a modified Mittag-Leffler distribution) arises. We also present a comparison of these two distributions in terms of an ergodicity-breaking parameter and show that the modified Mittag-Leffler distribution has a larger deviation from ergodicity. Some remarks on similarities between these results and observations in biological experiments are presented.
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