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Temporal correlation functions of concentration fluctuations: an anomalous case
Ariel Lubelski1, Joseph Klafter
1School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv, Israel. lubelski@post.tau.ac.il
The Journal of Physical Chemistry. B
|September 17, 2008
Summary
This study uses the continuous time random walk (CTRW) model to analyze multiparticle temporal correlation functions in systems with anomalous subdiffusion. Results show aging and ergodicity breaking, impacting how concentration fluctuations correlate over time.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Anomalous subdiffusion is observed in various complex systems.
- Continuous Time Random Walk (CTRW) models are used to describe anomalous transport phenomena.
- Aging and ergodicity breaking are key features of systems with non-stationary dynamics.
Purpose of the Study:
- To calculate multiparticle temporal correlation functions (CCF) of concentration fluctuations in systems exhibiting anomalous subdiffusion using the CTRW model.
- To investigate the impact of aging and ergodicity breaking on CCF.
- To explore the differences between time and ensemble averages of CCF.
Main Methods:
- Utilizing the Continuous Time Random Walk (CTRW) framework.
- Analytical calculations of multiparticle temporal correlation functions.
- Computer simulations based on the CTRW model.
Main Results:
- The CTRW model with non-stationary waiting times leads to anomalous subdiffusion.
- Aging effects cause temporal correlation functions to depend significantly on the initial measurement time.
- Ergodicity breaking is demonstrated through the divergence of time and ensemble averages of CCF.
Conclusions:
- The study provides a theoretical framework for understanding concentration fluctuations in aging systems.
- The observed ergodicity breaking may be experimentally verifiable.
- The findings contribute to the understanding of anomalous transport and complex system dynamics.
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