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Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential
Xudong Wang1, Yao Chen1, Weihua Deng1
1School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China.
Physical Review. E
|May 20, 2020
Summary
This study investigates how stochastic processes relax under confinement. We found that their relaxation dynamics depend on the velocity correlation function, offering insights into anomalous diffusion.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Stochastic processes are fundamental in modeling various physical phenomena.
- Understanding their response to external forces and confinement is crucial for characterizing their behavior.
Purpose of the Study:
- To investigate the relaxation dynamics of a generic stochastic process confined within a harmonic potential.
- To establish a relationship between the confined process's dynamics and the velocity correlation function of the unconfined process.
Main Methods:
- Analysis of ensemble- and time-averaged mean squared displacements.
- Utilizing scaling forms of the velocity correlation function for short and long time correlations.
- Generalizing findings across various anomalous diffusion models.
Main Results:
- The relaxation dynamics of confined stochastic processes are directly linked to their velocity correlation function.
- A unified approach is presented for both single-scaled (e.g., fractional Brownian motion) and multiscaled (e.g., Lévy walk) anomalous diffusion.
- The stationary value and relaxation behaviors are readily determined from the correlation function.
Conclusions:
- The study provides a general framework for understanding relaxation in confined stochastic systems.
- The findings are applicable to a wide range of anomalous diffusion processes, including those with active noise.
- This work offers a pathway to predict system behavior under spatial constraints based on intrinsic dynamics.
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