Condensed Matter > Statistical Mechanics
[Submitted on 4 May 2016 (v1), last revised 31 Jul 2016 (this version, v2)]
Title:Distributional Behavior of Diffusion Coefficients Obtained by Single Trajectories in Annealed Transit Time Model
View PDFAbstract:Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the diffusion coefficients are intrinsically random in non-equilibrium situations. Our findings pave the way for a theoretical understanding of distributional behavior of the diffusion coefficients in disordered systems.
Submission history
From: Takuma Akimoto [view email][v1] Wed, 4 May 2016 07:58:10 UTC (611 KB)
[v2] Sun, 31 Jul 2016 08:24:17 UTC (611 KB)
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