Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
By Andrey G. Cherstvy, Aleksei V. Chechkin, Ralf Metzler. 2013
296 citations recorded by the source corpus.
We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) ≃ |x|α, this process yields anomalous diffusion of the form 〈x2(t)〉 ≃ t2/(2−α). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement δ2(Δ)¯?> remains linear in the lag time Δ and thus differs from the corresponding ensemble average 〈x2(t)〉. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean-squared displacement δ2¯?> and its random features, i.e. the statistical distribution of δ2¯?> and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non-ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.
Subfields: Condensed Matter Physics, Mathematical Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/9adc03f7b55d31d3c0e6e78e3d8ad5d5e9b11c22
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
In Mathematical Physics
In Molecular Biology
Citations in the corpus
- Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion (2018, unknown): “heterogeneous diffusion processes [37, 38, 39, 40].”
- Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity (2014, background): “[20] A.”
- Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities (2016, background): “Heterogeneous diffusion processes employ a continuous, deterministic space dependence of the diffusivity and lead to nonergodic and aging dynamics [55,58,59].”