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Nonergodicity mimics inhomogeneity in single particle tracking
Ariel Lubelski1, Igor M Sokolov, Joseph Klafter
1School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel.
Physical Review Letters
|July 23, 2008
Summary
Statistical theories often use ensemble averages for anomalous diffusion. However, temporal averaging in single molecule tracking reveals simple diffusion with varying coefficients, creating an inhomogeneous system.
Area of Science:
- Physics
- Statistical Mechanics
- Physical Chemistry
Background:
- Anomalous diffusion theories typically rely on ensemble-averaged quantities like mean squared displacement.
- Single-molecule tracking experiments necessitate temporal averaging, posing a challenge to existing theories.
Purpose of the Study:
- To contrast ensemble averaging and temporal averaging in anomalous diffusion.
- To investigate continuous-time random walks with power-law waiting time distributions (0
Main Methods:
- Analysis of continuous-time random walks with power-law waiting time distributions.
- Comparison of ensemble-averaged mean squared displacement with temporally averaged mean squared displacement.
Main Results:
- Temporal averaging of mean squared displacement in this system leads to apparent simple diffusive behavior.
- Diffusion coefficients vary significantly between individual trajectories, indicating system inhomogeneity.
- An effective diffusion coefficient (Keff) emerges, dependent on trajectory length (T) as Keff ~ T^(alpha-1).
Conclusions:
- Temporal averaging in single-molecule tracking can obscure the underlying anomalous diffusion dynamics.
- The observed inhomogeneity arises from a distribution of diffusion coefficients among trajectories.
- The findings highlight the importance of considering averaging methods in interpreting diffusion data.
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