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Generalized Fokker-Planck equation for the active Ornstein-Uhlenbeck particle
Sanju S Pillai1, M Muhsin1, M Sahoo1
1University of Kerala, Department of Physics, Kariavattom, Thiruvananthapuram 695581, India.
Physical Review. E
|June 19, 2026
Summary
This study explores active Ornstein-Uhlenbeck particle dynamics in complex, non-Markovian environments. We developed a framework to analyze particle motion influenced by viscoelasticity and external forces like magnetic fields.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Complex Systems
Background:
- Understanding particle dynamics in complex fluids is crucial for fields like biophysics and materials science.
- Non-Markovian environments, characterized by memory effects, present unique challenges compared to simple diffusive systems.
- Active particles, capable of self-propulsion, exhibit complex behaviors influenced by their surroundings.
Purpose of the Study:
- To investigate the dynamics of an inertial active Ornstein-Uhlenbeck particle in a non-Markovian viscoelastic environment.
- To analyze the influence of external forces, including harmonic confinement and magnetic fields, on particle behavior.
- To develop a theoretical framework for describing particle motion in complex, memory-dependent media.
Main Methods:
- Modeling the particle's environment using the Jeffreys fluid framework to capture viscoelastic properties.
- Deriving the Fokker-Planck equation for specific cases and a generalized Fokker-Planck equation for the general non-Markovian framework.
- Obtaining the probability distribution function for various conditions, including free and confined motion with and without magnetic fields.
Main Results:
- Explicit derivation of the Fokker-Planck equation for active particle motion in a Jeffreys fluid.
- Development of a generalized Fokker-Planck equation applicable to arbitrary memory kernels in non-Markovian environments.
- Characterization of the probability distribution function under diverse conditions, revealing insights into particle behavior.
Conclusions:
- The developed theoretical framework provides a robust method for analyzing active particle dynamics in non-Markovian environments like polymer solutions and mucus.
- This research facilitates the study of relaxation phenomena in confined geometries and the response of active particles to external fields.
- The findings are applicable to understanding complex fluid behavior and designing active matter systems.
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