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Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity
Takashi Uneyama1, Tomoshige Miyaguchi2, Takuma Akimoto3
1Center for Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan.
Physical Review. E
|April 20, 2019
Summary
We investigated the Ornstein-Uhlenbeck process with fluctuating diffusivity (FD). Our findings reveal unique relaxation behaviors distinct from conventional models, offering new insights into complex dynamics.
Area of Science:
- Statistical Physics
- Complex Systems Dynamics
Background:
- The Ornstein-Uhlenbeck process models particle dynamics with a restoring force.
- Fluctuating diffusivity (FD) is crucial for modeling heterogeneous environments or internal degrees of freedom.
Purpose of the Study:
- To analyze the relaxation behavior of the Ornstein-Uhlenbeck process under fluctuating diffusivity.
- To develop a general theoretical framework for systems with FD.
Main Methods:
- Utilized functional integral expressions and the transfer matrix method.
- Derived relaxation functions based on eigenvalues and eigenfunctions of the transfer matrix.
Main Results:
- Developed a general theory for relaxation functions in FD processes.
- Obtained analytic expressions for relaxation functions in two-state and OU-type FD models.
- Identified distinct relaxation behaviors compared to generalized Langevin equations.
Conclusions:
- The Ornstein-Uhlenbeck process with FD exhibits unique relaxation dynamics.
- The developed theory provides a framework for analyzing complex relaxational systems.
- This work advances the understanding of dynamics in heterogeneous or internally complex systems.
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